Unified origin for visible and dark matter in a baryon-symmetric universe from a first-order phase transition

0.17 MB·English

by  Raymond R. Volkas

NuclearPhysicsB
Proceedings
Supplement
NuclearPhysicsBProceedingsSupplement00(2013)1–5
Unified origin for visible and dark matter in a baryon-symmetric universe from a
first-order phase transition
RaymondR.Volkas
ARCCentreofExcellenceforParticlePhysicsattheTerascale,SchoolofPhysics,TheUniversityofMelbourne,Victoria3010,Australia
3
1
0
2

n Abstract
a
J In a baryon-symmetric universe, the baryon asymmetry observed for visible matter is matched by an equal and
4 oppositeasymmetryfordarkmatter,therebycloselyconnectingthenumberdensitiesofbothtypesofmatter.Thisisa
2 necessarysteptowardsthegoalofexplainingthemysteryofwhythevisibleanddarkmatterdensitiesareobservedto
besimilar.Inthistalk,awayofproducingsuchauniversefrombubblenucleationduringafirst-orderphasetransition

]
isreviewed. Theprocessisananalogofelectroweakbaryogenesis.
h
p
Keywords: asymmetricdarkmatter,baryogenesis,first-orderphasetransition,baryon-symmetricuniverse,
-
p anomaloussymmetry
e PACS:95.35.+d,98.80.Cq
h
[

2 1. Introduction is that the DM is a new particle with an electroweak-
v
scale mass, typically a Majorana fermion such as the
5 The fact that the cosmological mass density of ordi-
neutralino of supersymmetric theories, whose cosmo-
6
naryorvisiblematter(VM)todayisonlyaboutafactor
9 logical density is determined by a weak-scale annihi-
of five different from the mass density of dark matter
3 lation cross-section. As the temperature of the uni-
. (DM), verse drops below the WIMP mass, the creation of
1
0 Ω (cid:39)5Ω , (1) WIMPsbecomesenergeticallydisfavoredandtheirden-
d v
3 sitydropsthroughBoltzmannsuppressionuntiltheyde-
1 suggestsacommonoriginforboth.Inthistalk,Ireview couple from the VM plasma. With a weak-scale anni-
:
v workperformedwithK.PetrakiandM.Trodden[1]on hilation cross-section, it turns out that the WIMPs de-
i a model that (partially) explains this fact from the uni- couple when their mass density is in the correct range
X
fied production of VM and DM through the agency of toexplainthecosmologicalDMobservations. Thissce-
r
a bubble nucleation dynamics during a first-order phase narioisconsideredtobeattractivebecausetheexistence
transition in the early universe, an analog of the elec- ofweakly-interactingelectroweak-scaleparticlesismo-
troweak baryogenesis mechanism [2]. It is a particu- tivated by independent particle physics problems. The
larscenariodrawnfromthespecialclassofasymmetric neutralino, for example, is required by the supersym-
DMmodels[3]whichfeaturea“baryon-symmetricuni- metricsolutionofthegaugehierarchyproblem.
verse”[4]. Thisideaisexplainedbelow.
However, the WIMP hypothesis leaves unexplained
WestartbydiscussingthepopularWeaklyInteracting
why the DM density is so similar to the VM den-
MassiveParticle(WIMP)hypothesisforDM.Theidea
sity. The latter is not determined by the physics of
weak-scale annihilation. Rather, it is due to the exis-
tenceofthecosmologicalbaryonasymmetry: someas-
Emailaddress:[email protected](RaymondR.
Volkas) yet unknown physics in the early universe caused the
RaymondR.Volkas/NuclearPhysicsBProceedingsSupplement00(2013)1–5 2
baryonstooutnumbertheantibaryonsbyaboutonepart Hereisthesymmetryprinciple[7]: Calltheordinary
in1010. Thebaryon-antibaryonannihilationswhichde- baryonnumberB ,andletB standardfortheDMana-
1 2
plete those species’ number densities at temperatures log. Formtheorthogonallinearcombinations
below their masses switch off not because the interac-
B ≡ B −B
tions become too weak, but because the baryons even- 1 2
X ≡ B +B . (2)
tually have no antibaryons to annihilate with. The ex- 1 2
cessbaryonsformtheVMintheuniversetoday. Weak- Now demand that B is either an exactly or essentially
scale annihilation that becomes ineffective through de- conservedquantumnumber,whileX isviolatedathigh
couplingcomparedwithstrong-sectorannihilationthat energiesandintheearlyuniverse. (By“essentiallycon-
switches off because of a particle-antiparticle asym- served” we mean we remain open to the existence of
metry: these are very different processes, involving extremelyweaknon-conservingprocesses,suchasvery
different forces and circumstances, yet in the WIMP slow proton decay, but these are so weak that they are
paradigm they are required to coincidentally produce cosmologically irrelevant.) Dynamics that violates X
similar relic mass densities. Acknowledging this nec- through out-of-equilibrium processes that also violate
essary coincidence motivates that an alternative to the C andCPwill,accordingtotheSakharovanalysis[8],
WIMPhypothesisbegivenseriousconsideration. produce an X asymmetry. But no B asymmetry devel-
Theobviousalternativeissimplytosupposethatthe ops,sowehavethat
DM density is also due to a particle-antiparticle asym-
∆B =∆B =∆X/2. (3)
metry,andthatthereisadynamicalconnectionbetween 1 2
the visible and dark sectors that makes the asymme- The quantity B may be thought of as a generalized
tries similar, or possibly even identical. This is the baryon number. At low energies and in the late uni-
“asymmetricDM”hypothesis. TheideaisthattheDM verse, X violation becomes very weak, and B and B
1 2
consists of stable relics from a hidden sector that pos- becomeindividuallyconserved.Inthevisiblesector,B
1
sesses an analog of baryon number. The dark sector conservationensuresthe(essential)stabilityofprotons
may be its own complicated world, described by some andthisaccountsforthebulkoftheVMdensity. Elec-
kind of gauge theory. For the special case of “mirror tric charge and angular momentum conservation also
matter”[5], thedarkgaugetheoryisisomorphictothe make the electron and, respectively, the lightest neu-
standardmodel(SM),butingeneralitisdifferent.Inthe trino stable. In the dark sector, B conservation en-
2
low-energyworldofthelateuniverseinwhichwelive, sures the stability of at least one species. For other
wecametoknowoftheothersectorthroughtheneces- reasons, there may be other stable dark species. Non-
sarily common gravitational interaction. But the simi- perturbative sphaleron effects may reprocess some of
lardensitiessuggestthattherearealsonon-gravitational theseasymmetriesinoneorbothsectors.
connectionstobediscoveredbetweenourworldandthe The requirement that B is never violated is a strong
darkworld. InasymmetricDMmodels,thesimilarVM one. Tojustifysuchanimposition, itisnaturaltotake
andDMasymmetriespointtoaDMparticlemassinthe U(1) to be a gauge symmetry, while U(1) is global.
B X
fewGeVregime. TheDAMA,CoGeNTandCRESST In that case, anomaly-freedom suggests that B should
anomaliesprovidesomeencouragementtotakethisse- ratherbereplacedbyB−L,whichisindeedwhatwedo
riously[6]. below. Any such model must be constructed to ensure
A baryon-symmetric universe is one that contains a thataglobalU(1) isproducedafterthegaugedU(1)
B B−L
DM asymmetry that is exactly the opposite of the VM isspontaneouslybroken. Thereisastandardwaytodo
asymmetry, so it is a special case of asymmetric DM. this,asexplainedinRef.[1].
It is attractive because the strong connection between The first consideration in building a model for a
thetwoasymmetriesisdrivenbyasymmetryprinciple baryon-symmetricuniverseisthedynamicsofX asym-
ratherthanbythespecificsofsomedynamicalscheme. metry generation. We may borrow the essential idea
Indeed, many different theories can produce a baryon- fromeachknownwayofgeneratinganordinarybaryon
symmetric universe, and this talk is about only one of asymmetry,andreuseittoproduceanonzero X. Well-
them.Establishingaconnectionbetweenthevisibleand studied schemes include out-of-equilibrium heavy par-
darkasymmetriesisanecessarysteptowardsthegoalof ticledecays,Affleck-Dinedynamics[9],andbubblenu-
acompleteunderstandingofthesimilarvisibleanddark cleationduringafirst-orderphasetransition(asusedin
massdensities.Onealsoneedsatheoryfortheoriginof electroweak baryogenesis). We employ the latter here.
the few-GeV DM mass scale, but that important prob- See Refs. [7, 10] for papers on baryon-symmetric uni-
lemisbeyondthescopeofthistalk. versemodels.
RaymondR.Volkas/NuclearPhysicsBProceedingsSupplement00(2013)1–5 3
We first briefly recall how electroweak baryogene- Fields SU(2)G U(1)B−L U(1)X U(1)D
sis works. Above the critical temperature for the elec- gauged gauged anom. gauged
troweakphasetransition,theHiggsvacuumexpectation ψ 2 0 -2 0
L
valueiszeroandweaksphaleronsinducecertainrapid g ψ 1 0 -2 0
1,2R
B1-violating processes. In electroweak baryogenesis, ϕ 2 0 0 0
the phase transition is required to be strongly first or- f 1 -1 -1 0
v L,R
der: bubblesofbrokenphasearenucleatedatthecriti- ν 1 -1 -1 0
R
caltemperaturewithinthepre-existingsymmetricphase χ 2 1 -1 0
universe. Sufficiently large bubbles grow rapidly, and d ξ 2 0 0 1
L,R
the passage of the bubble walls produces the required ζ 1 -1 1 1
L,R
departure from thermal equilibrium. Top quark inter-
actions with the moving walls violate C and CP, and
sphaleron-inducedB violationcontinuesintheregions Table1: Thechargeassignmentsunderthenewsymmetriesinthe
1
model,whereg,v,andddenotethegenerative,visibleanddarksec-
ofsymmetricphase. Theseingredientsworktogetherto
tors,respectively. ThemodelconsistsoftheSMfields,thefieldsin
producea B1-asymmetricuniverseoncethephasetran- thistableandanotherscalarthatbreaksthegaugedU(1)B−L intoa
sitionhasbeencompletedandtheuniverseisfullyinthe globalbaryonnumbersymmetry. Threeright-handedneutrinosare
brokenphase.Inthenextsectionwedescribehowthese neededtocancelthecubicB−Lanomaly,andanevennumberoffam-
iliesoftheψfermionsisrequiredtoensuretheabsenceofaWitten
dynamics may be recast to produce an X-asymmetric,
anomaly.Thegenerative-sectorfieldϕgainsanonzeroVEVduringa
butB-symmetric,universe. first-orderphasetransition,whilethedark-sectorscalarχalwayshas
azeroVEV.ThefieldsfandχfacilitatethetransferoftheXasymme-
trytothevisibleanddarksectors.ThestableDMisformedfromthe
vector-likefermionsξandζ,whichform“atomic”two-bodybound
2. Themodel
statesthroughtheU(1)Ddarkelectromagnetism.
Themodelconsistsofthreesectors: visible, “gener-
ative” and dark. The visible sector is simply the SM, two right-handed components are singlets. Both chi-
extended to include a gauged U(1) , which means ral components carry X charges, but the fact that only
B−L
we include three right-handed neutrinos in the visible theleft-handedonesfeeltheSU(2) interactionscauses
G
particle spectrum. It also includes a vector-like sterile U(1) to be anomalous. There must be an even num-
X
fermion f whose role is explained below. The genera- ber of families of the ψ fermions to ensure absence
tive sector, to be described shortly, is the engine room of a Witten anomaly [11], the minimum number be-
ofXasymmetrycreation.OncenonzeroXhasbeencre- ing two. The generative sector also contains an SU(2)
ated by the dynamics of that sector, it is transferred to scalar doublet ϕ, whose role is to spontaneously break
the visible sector and the dark sector. The dark sector SU(2) in a strongly first-order phase transition. Be-
G
ofourmodelhasthegaugesymmetryU(1) ,aswellas causetheSU(2) isanexoticgaugeinteraction,wecan
D G
the U(1) it shares with the visible sector. The local make the phase transition as strongly first-order as we
B−L
U(1) symmetryisnotspontaneouslybroken,soitcan wish by choosing the scalar potential parameters ap-
D
be thought of as a dark sector version of electromag- propriately. Recall that this freedom is not available
netism. It is needed to annihilate away the symmetric for SU(2) breaking in the SM, because the parameter
L
part of the dark plasma, leaving the excess dark “an- choice required to produce a standard Higgs boson of
tibaryons” as the relic DM. The symmetries and field the observed mass is not consistent with a first-order
contentofourmodelaresummarizedinTable1. electroweak phase transition (so electroweak baryoge-
The generative sector is constructed to make U(1) nesiscanworkonlywithinsomeSMextensions). The
X
anomalous, with sphaleron transitions associated with twofamiliesofgenerativeψfermionsYukawacoupleto
a new SU(2) gauge interaction providing the neces- ϕinaC-andCP-violatingway.
G
saryviolationof X conservation. Thisstructureisbor- We now describe the dynamics of asymmetry cre-
rowedfromelectroweakbaryogenesis,wheretheU(1) ationandtransfertothevisibleanddarksectors,which
B1
current has a weak-isospin SU(2) anomaly, and weak servesalsotoexplaintherolesoftheexoticparticles f,
L
sphalerons mediate processes that violate B conser- χ, ξ and ζ. At a critical temperature somewhat above
1
vation. The fermions ψ in the generative sector have the electroweak scale, the ϕ field develops a nonzero
a similar chirality structure to that of ordinary quarks vacuum expectation value (VEV) through a strongly
and leptons with respect to weak interactions: the left- first-order phase transition, which proceeds via bubble
handed ψ’s are placed in an SU(2) doublet, while the nucleation of the broken phase. In the regions of un-
G
RaymondR.Volkas/NuclearPhysicsBProceedingsSupplement00(2013)1–5 4
broken phase SU(2) sphaleron effects cause rapid X- One important requirement is that the dark photonic
G
violating processes to occur, while such effects are ab- radiation created from the annihilation of the symmet-
sent in the regions of broken phase. The ψ fermions ricpart ofthedarkplasma doesnotspoilbig bangnu-
interact with the fast-moving ϕ bubble walls in a C- cleosynthesisthroughanunacceptablylargeincreasein
and CP-violating way. Emulating electroweak baryo- theexpansionrateoftheuniverseoverthestandardsce-
genesis, after the phase transition has been completed nario. Theamountofdarkradiationisgovernedbythe
thesecircumstancesleaveaplasmawithanX asymme- number of degrees of freedom in the dark sector that
try,carriedbytheψ particles.TheYukawainteractions undergo the annihilations. The constraint is therefore
L
ψ¯ χf +H.c.thentransfertheasymmetryviaψ decay anupperbound[1]
L R L
to the visible sector vector-like sterile fermions f and (cid:18) g (cid:19)
the dark sector scalar χ. Gauge invariance dictates the gd,dec (cid:46)18.6 11v0,d.e2c5 (6)
multiplet assignments of these particles. Since f and
whereg andg arethedegreeoffreedomcounts
χ carry equal and opposite B−L charges, the baryon- d,dec v,dec
inthedarkandvisiblesectors,respectively,atthetime
symmetric feature is preserved through the transfer.
the two sectors decouple from each other in the early
Notethatχdoesnotcarrydarkelectromagneticcharge.
universe. The18.6figurecomesfromboundingtheex-
The fields f Yukawa couple to the SM lepton dou-
R tra radiation to be at most the equivalent of one addi-
blets through the standard Higgs doublet, reprocessing
tionalneutrinoflavor. Thedarksectorofthemodelde-
theasymmetryitcarriesintothosefields.Throughother
scribedabovehasg =16.5,soitpassesthetest.
SM interactions, and weak sphalerons, the asymmetry d,dec
Another constraint arises from ensuring successful
spreadsthroughoutthevisiblesector.
large scale structure formation. As well as explaining
Thedarksectormustbelargerthanthescalarmulti-
various gravitational anomalies in the present day uni-
pletχ,becausethatfieldisnecessarilyimmunefromthe
verse, such as flat galactic rotation curves, DM is also
darkelectromagneticforceweneedtousetoannihilate
neededtoseedthegrowthofstructureintheearlyuni-
awaythesymmetricpart. Thisrequirestheexistenceof
verse. In the standard cold DM scenario, structure be-
theU(1) -chargedvector-likefermionsξ andζ, which
D ginstoformintheDMsoupassoonasmatterstartsto
Yukawacoupletoχthroughtheinteractions
dominateoverradiation. Thevisiblematterisstillion-
ξ¯LχζR+(L↔R)+H.c. (4) izedatthisstage, andtherelativelystrongelectromag-
Wechoosethefreemassparameterstomakeχdecouple netic force prevents the gravitational growth of struc-
anddecaythroughthisinteractionintotheξandζ dark ture in that sector. Baryonic structure growth is there-
fermions. Theunbrokendarkelectricchargeconserva- fore delayed until neutral atoms form and the ordinary
tionworkswiththenowessentiallyrestoredB conser- photonsdecouple, butbythentherearealreadysignif-
2
vation to make all of these fermions stable (assuming icant DM overdensities to facilitate the growth of in-
there is only one family). The symmetric part annihi- homogeneities in ordinary matter. To ensure that this
lates into dark photons, leaving an excess of ξ¯ and ζ successfulscenarioisnotspoiled,wemustrequirethat
particlestobetherelicDM.Infact,theDMtodayisin darkphotondecouplinghappensnolaterthanthepoint
the form of “atomic” bound states of ξ¯ and ζ, with the of matter-radiation equality. It turns out that this leads
bindingduetotheU(1) force. TheDMisthusakind toconstraintsonthereducedξ¯,ζmassandthedarkfine
D
of“darkhydrogen”,thoughtherearesomedissimilari- structureconstantαDthatarequiteeasytosatisfy[1].
ties:thereisnodarknuclearphysics,andthereneednot Finally, the Bullet cluster observations are argued
be such a large difference in mass between ξ¯ and ζ as to provide an upper bound on the DM self-interaction
thereisbetweentheprotonandtheelectron. Toobtain cross-sectionσ[12]:
theobservedDMmassdensity,wemusthave σ
(cid:46)1cm2/g, (7)
Ω m
m +m (cid:39)0.3m d (cid:39)1.5GeV, (5) d
ξ ζ pΩ wherem isthemassoftheDMparticle.Fortheatomic
v d
wherem istheprotonmassandthe0.3factorisdueto DM of the described model, the cross-section is deter-
p
weaksphaleronreprocessinginthevisiblesector. mined by the geometric size of the DM atoms. To en-
suresufficientlytightlyboundDMatoms,thebound
3. Constraints α >0.3 (8)
D
Theparametersinthemodelmustbechosentoobey is indicated [1]. On the face of it, this is the strongest
certaincosmologicalandastrophysicalconstraints. constraintonthemodel.
RaymondR.Volkas/NuclearPhysicsBProceedingsSupplement00(2013)1–5 5
4. Signatures References
Themodelpossessesfeaturesthatcanbesearchedfor [1] K.Petraki, M.TroddenandR.R.Volkas, JCAP1202(2012)
incollideranddirectDMdetectionexperiments.Onthe 044.
[2] Forareviewsee,A.RiottoandM.Trodden,Ann.Rev.Nucl.
colliderside, thegaugedU(1) impliestheexistence
B−L Part.Sci.49(1999)35.
ofaZ(cid:48) bosonthathasasignificantinvisiblewidthinto [3] Forarecentreviewsee, H.DavoudiaslandR.N.Mohapatra,
DM. The B − L breaking scale could be low enough NewJ.Phys.14(2012)095011,andsee[1]foranextensivelist
for such a particle to be observable at the LHC. The ofreferencestoasymmetricdarkmattermodels.
[4] S.DodelsonandL.M.Widrow,Phys.Rev.Lett.64(1990)340;
scalarsectorofthetheoryisquiterich,andwillingen-
Phys.Rev.D42(1990)326;Mod.Phys.Lett.A5(1990)1623.
eralleadtomodificationsofSMHiggsbosonproperties [5] See, for example, R. Foot, H. Lew and R. R. Volkas, Phys.
and of course the existence of additional spin-0 parti- Lett.B272(1991)67;Z.Berezhiani,D.Comelli,F.L.Villante,
Phys.Lett.B503(2001)362;A.Yu.IgnatievandR.R.Volkas,
cles. DirectDMdetectionexperimentsarerelevantfor
Phys.Rev.D68(2003)023518;R.FootandR.R.Volkas,Phys.
thismodelbecauseoftheZ(cid:48)interaction. Onemaycom-
Rev.D68(2003)021304;Phys.Rev.D69(2004)123510;Z.
putethattheZ(cid:48)-inducedspin-independentDM-nucleon Berezhianietal.,Int.J.Mod.Phys.D14(2005)107;P.Ciar-
cross-sectionis[1] celluti,Int.J.Mod.Phys.D14(2005)187;Int.J.Mod.Phys.D
14(2005)223;R.Foot,Phys.Rev.D82(2010)095001;Phys.
(cid:18)g (cid:19)4(cid:32)0.7TeV(cid:33)4 Rev.D86(2012)023524; arXiv:1211.1500; J.-W.Cuietal.,
σSI (cid:39)10−44cm2 B−L , (9) Phys.Rev.D85(2012)096003.
0.1 M
B−L [6] For citations to the original literature and an analysis of how
where g and M are the Z(cid:48) gauge coupling con- theseresultsmaybereconciledwithhiddensectordarkmatter,
B−L B−L seeR.Foot,arXiv:1209.5602.
stantandmass,respectively. Forreasonablechoicesof
[7] N.F.Bell,K.Petraki,I.M.ShoemakerandR.R.Volkas.Phys.
theseparameters,theboundsfromXENON100[13]and Rev.D84(2011)123505;L.J.Hall,J.March-RussellandS.M.
CDMS II [14] are easily met. The DM-nucleon cross- West,arXiv:1010.0245.
[8] A.D.Sakharov,Pisma,Zh.Eksp.Theor.Fiz.5(1967)32.
section may be enhanced in a variant of this model,
[9] I.AffleckandM.Dine,Nucl.Phys.B249(1985)361;M.Dine,
whereU(1)Disspontaneouslybrokenandthenowmas- L.RandallandS.Thomas,Nucl.Phys.B458(1996)291.
sive dark photon kinetically mixes with the ordinary [10] V.A.Kuzmin,Phys.Part.Nucl.29(1998)257;R.Kitanoand
photon. I.Low,Phys.Rev.D71(2005)023510;hep-ph/0503112;P.-H.
Gu,Phys.Lett.B657(2007)103; P.-H.Gu,U.SarkarandX.
Zhang,Phys.Rev.D80(2009)076003;H.An,S.-L.Chen,R.N.
5. Conclusion MohapatraandY.Zhang,JHEP03(2010)124;H.Davoudiasl,
D. E. Morrissey, K. Sigurdson and S. Tulin, Phys. Rev. Lett.
105 (2010) 211304; P.-H. Gu, M. Lindner, U. Sarkar and X.
Thesimilarvisibleanddarkmatterdensitiessuggest
Zhang,Phys.Rev.D83(2011)055008;J.J.HeckmanandS.-J.
a common origin for both types of matter, as can be
Rey,JHEP1106(2011)120;D.H.OakninandA.Zhitnitsky,
obtained in asymmetric DM models in general and the Phys.Rev.D71(2005)023519;G.R.FarrarandG.Zaharijas,
baryon-symmetricspecialcasesinparticular.Abaryon- Phys.Rev.Lett.96(2006)041302;C.CheungandK.M.Zurek,
Phys.Rev.D84(2011)035007;B.vonHarling,K.Petrakiand
symmetricuniversehastheDMcarryingageneralized
R.R.Volkas,JCAP1205(2012)021;J.March-RussellandM.
baryon asymmetry that cancels the asymmetry in the McCullough,arXiv:1106.4319;K.KamadaandM.Yamaguchi,
visiblesector,andleadstoaverytightrelationshipbe- arXiv:1201.2636.
tween ordinary and DM enforced by a simple symme- [11] E.Witten,Phys.Lett.B117(1982)324.
[12] M.Markevitchet.al.,Ap.J.606(2004)819;S.W.Randallet
tryprinciple. Inthistalk,abaryonsymmetricuniverse
al,Ap.J.679(2008)1173.
was described that has the equal and opposite visible [13] XENON100Collaboration,E.Aprileet.al.,Phys.Rev.Lett.107
and dark asymmetries produced by an analog of elec- (2011)131302.
troweakbaryogenesis. Cosmologicalandastrophysical [14] CDMS-IICollaboration,Z.Ahmedet.al.,Phys.Rev.Lett.106
(2011)131302.
constraints were examined, and signatures for collider
and direct DM detection experiments very briefly dis-
cussed.
Acknowledgments
This work was supported in part by the Australian
ResearchCouncil. Theauthorthankshisexcellentcol-
laborators K. Petraki and M. Trodden, and warmly ac-
knowledgesthehospitalityandsupportoftheorganizers
oftheCosPA2012symposium.