Nucleosynthesis constraints on the faint vector portal

0.14 MB·English

by  Anthony Fradette

EPJWebofConferenceswillbesetbythepublisher
DOI:willbesetbythepublisher
c Ownedbytheauthors,publishedbyEDPSciences,2015
(cid:13)
Nucleosynthesis constraints on the faint vector portal
AnthonyFradette1,MaximPospelov1,2,JosefPradler3,a,andAdamRitz1
1DepartmentofPhysicsandAstronomy,UniversityofVictoria,Victoria,BCV8P5C2,Canada
2PerimeterInstituteforTheoreticalPhysics,Waterloo,ONN2J2W9,Canada
3InstituteofHighEnergyPhysics,AustrianAcademyofSciences,A-1050Vienna,Austria
5
1
0
Abstract. New Abelian U(1) gauge bosons V can couple to the Standard Model through mixing of the
′ µ
2
associated field strength tensor V with the one from hypercharge, FY . Here we consider early Universe
µν µν
n sensitivitytothisvectorportalandshowthattheeffectivemixingparameterwiththephoton,κ,isbeingprobed
a forvectormassesintheGeVballparkdowntovalues10 10 .κ.10 14wherenoterrestrialprobesexist. The
− −
J
ensuingconstraintsarebasedonadetailedcalculationofthevectorrelicabundanceandanin-depthanalysisof

2 relevantnucleosynthesisprocesses.

]
h
p
1 Introduction the following we will concentrate on a Stückelberg ori-
-
p gin of m that allows to maintain gauge invariance in
V
e The origins of our Universe may well be rooted in infla- U(1) withoutcomplicatingthephenomenologybyhidden
′
h tion or alternative cataclysmic scenarios that regard the
Higgsparticlesh;seee.g.[4]forthephenomenologyand
[ ′
veryearliestmomentsofexistence. However,despitethe
[5]forcosmologicalconstraintsonthelatterscenario.

1 impressive success of observational cosmology over the
The SM decay modes of V are well known. When
v past decades, the earliest true direct window into the be-
hadronicdecaysarekinematicallyaccessible,onecanuse
9 ginningsremainobservationsoflightelementabundances.
experimentaldataontheR-ratiotoinfercouplingstopho-
5
Theyconcerntheepochofprimoridalnucleartransforma-
4 tonsinthetime-likedirection,andhencetodeterminethe
tions at cosmic times t & 1s. The overall concordance
0 decayrateΓ andallbranchingratios.Belowthedi-muon
V
0 of the Big Bang nucleosynthesis (BBN) predictionswith threshold and for m > 1MeV the vector V decays to
V
. theobservationallyinferredprimordialvaluesisoneofthe
1 electron-positron pairs only, thereby setting its principal
0 mostimpressivesuccessesofmoderndaycosmologyand lifetime,
5 particle physics. Today, BBN is used as a toolboxto put
1 models of new physics to a stringent test [1], whenever 3 1GeV 10 12 2
v: they predictsome interferencewith the the standardpro- τV ≃ κ2αm =270s× m κ− ! , (2)
i cessesintheobservablesectoratt&1s. V V
X
Undertheassumptionofacanonicalsequenceofcos-
whereαiselectromagneticfinestructureconstant. Inthe
r
mologicalevents,theUniverseemergedfrominflationand
a followingthecosmologicalconsequencesofU(1) vectors
′
baryogenesismuchpriortoBBN.Suchsequencethenal-
with masses in the MeV-GeV range, and lifetimes long
lowsonetoputstringentconstraintsonveryweaklyinter-
enoughforthedecayproductstodirectlyinfluenceprimor-
actingsectorsofnewphysicsbeyondtheStandardModel
dial nucleosynthesis are explored. These vectors have a
(SM). The kinetic mixing of a new U(1) vector V with
′ µ parametricallysmallcouplingto theelectromagneticcur-
hypercharge FY Vµν is of particular interest as the mix-
µν rent,andthusanextremelysmallproductioncrosssection
ingwiththephotonleadstonumerousexperimentalcon-
for e+e Vγ, σ κ2πα2/s 10 54cm2 wherewe
− prod −
sequences and much attention was devoted to this vector → ∼ ∼
took √s = 200 MeV and κ = 10 12 from above. Such
−
portalinrecentyears[2].Belowtheelectroweakscale,the
smallcouplingsrenderthesevectorstatescompletelyun-
couplingofV totheSMisessentiallygivenbyitsmixing
detectableinterrestrialparticlephysicsexperiments.
withthephoton[3],
Despitethetinyproductioncrosssection,anycharged
κ SM state that is populated in appreciable number in the
= F Vµν =eκV Jµ . (1)
LV −2 µν µ em early Universe at temperature T mV may yet emit V.
∼
With the above ballpark numbers in (2), parametric es-
With κandm beingtheonlyfreeparameters,themodel
V timates suggest that an amount of MeV/baryon may be
provides a simple, and technically natural prototype sce-
storedinV-particles.FollowedbylatedecaysbacktoSM
narioforalight,weaklyinteractingnewparticlesector.In
states, visible energy is therefore being injected into the
ae-mail:[e-mail] primordialplasma atlevelsthatare probedbyBBN. The
EPJWebofConferences
abundancecanbeperformedexplicitly,
¯
l
κ Y(e) = 9 m3VΓV→ee¯. (5)
V 4π(Hs)
Aµ Vµ T=mV
While further leptonic production channels are easy
l
time to be included into (5), hadronicproductionchannelsre-
quire assumptions about the primordial hadron gas and
Figure1. Darkphotoninversedecaysaretheleadingcontribu- the strength of interaction with photons, denoted by α .
eff
tion to sub-Hubble production rates inthe calculation of the V At temperatures above the QCD confinement scale T
c
∼
relicdensity. 200MeVlightquarksaredeconfinedandindividualquark
contributionscanbeaddedtoY inastraightforwardman-
V
ner. BelowT onemayuseafreegasofmesonsasanap-
c
proximation to the hadronic (non-baryonic)particle con-
early Universe is therefore likely to be the only “labora- tent in the early Universe. The production via inverse
tsomryal”lewrhaererebseuincghpvreorbyedda.rkHeprheowtoensrewpiotrhtoκn∼th1e0d−e1t2aialnedd tchheanrgbeedinpciolundeadnduskinaognadseccaalayrsQ{πE+Dπ−m,oKd+eKlw−}ith→effVectciavne
analysisperformedin[7]wherealsoCMBlimitsoneven couplingstrengthslikeαπeffπ(mV)=κ2αππ(√s=mV)where
laterdecayswereconsidered.Previouspartialdiscussions αππ is extracted from BaBar cross section measurements
ofcosmologicalsignaturesofdecayingdarkphotonsmay ofe+e− γ∗ π+π−(γ)[11],andsimilarlyforcharged
→ →
alsobefoundin[5,6]. kaons[12].
Inthefollowingweassumenootherlightstatesχthat Finally,thereisapossibilityofresonantproductionof
are charged under U(1). Therefore, there are no decays V by virtue of the thermalbath. Such in-mediumeffects
′
V χχ¯ thatpotentiallydrainvisible modesandthereby maybecastintoaneffectivemixingangle,
→
ameliorate the derived limits from BBN. Using some re- κ
κ = , (6)
centinsightaboutthein-mediumproductionofdarkvec- T,L 1 Π /m2
tors[8,9](seealso[10])wefirstdiscusstheproductionof | − T,L V|
darkvectorsinthenextsectionandexploreconstraintson with Π being the transverse (T) and longitudinal (L)
T,L
V-decaysintoSMinSec.3beforeconcludingwithSec.4. photonpolarizationfunctionsin the primordial, isotropic
plasma.TheexpressionsforΠ cane.g.befoundin[13];
T,L
the longitudinal polarization function [8] used here is,
2 Abundance prior to decay Πhere = m2/(ω2 m2)ΠRef.[13] and ω is the (dark) pho-
L V − V L
tonenergy.Equation(6)informsusabouttheconditionof
Therelicabundanceofweaklycoupleddarkphotonsprior
resonantdarkphotonproduction,
totheirdecayisobtainedthroughacalculationoftheleak-
age from the observable sector to the hidden sector with ReΠ (ω,T )=m2. (7)
T,L r,T,L V
sub-Hubblerates, Γ /H 1. This“freeze-in”process
prod
≪
is dominatedby inversedecaysof V, throughthe coales- TheconditiondependsontemperatureT asΠ arepro-
T,L
cence of e , µ ..., and, similarly, throughhadroniccon- portional to the plasma frequency, ω (T). Most impor-
± ± P
tributions;seetheillustrationinFig.1. tantly,theresonancetemperatureT (ω)asafunctionof
r,T,L
The Boltzmannequationfor the totalnumberdensity frequencyωisparametricallylargerthanm withamini-
V
ofV takestheform mumfrequencyatwhichtheresonancecanhappen,
n˙ +3Hn =C. (3) 3 1/2
V V T =m 8m . (8)
r,min V"2πα# ≃ V
The righthandside is the collision integraland provided
thatVneverreachesthermalequilibrium,itgivesthenum- Thus resonances occur at parametrically larger tempera-
ber ofV states emittedperunitvolumeandunittime. In tures (by α−1/2) than mV, for which H(T) is significantly
theMaxwell-BoltzmannapproximationfortheSMdistri- largerthanatT mV atwhichtheV freeze-inproduction
≃
butionfunctions,andin thelimitthatonlyelectronscoa- has its biggest contribution. Therefore, resonant contri-
lesce, the integrationcan be done analytically [5, 7] (see butions to YV do not alter the picture drastically though
also[6]) numericallytheymayconstituteasmuchas30%.
Afterproduction,themomentumofV redhiftsquickly
3 sothatatthetimeofdecaytheenergyofV istogoodap-
C Γ m2TK (m /T). (4)
≃ 2π2 V→ee¯ V 1 V proximationgivenbytherestmass, EV = mV. Thedecay
deposits this energy into leptons, hadrons, and hadronic
Here, Γ = κ2αm /3 is the decay width of V to elec-
V ee¯ V resonances. The energy prior to decay that is stored per
trons, up→to corrections(m /m )2 and K is the modified
e V 1 baryonisthereforegivenby
Besselfunctionofthesecondkind.Intermsofthenumber
s
of V particlesnormalizedto entropydensity, YV = nV/s, Ep.b. =mVYV 0 , (9)
the cosmic time integral in (3) for the final “freeze-in” nb,0
DarkMatter,HadronPhysicsandFusionPhysics
where n /s = 0.9 10 10 is the baryon-to-entropyra- 101 ..
b,0 0 × − p(p¯)
tio today. Equipped with Ep.b. as a function of mV and n(n¯) V →hadr.
κ followingthe detailed calculationsof the V “freeze in” π+(π−)
abundance in [7], we may now explore its consequences K+(K−)
)
forBBN. ay KL
c
e
d
c 1
3 V-decaysduring BBN ni
ro hEemi/mV
d
a
Primordial nucleosynthesis predictions are affected for h
(
darkphotondecayswithcosmiclifetimet & 1sorlarger. s/
e
Ensuingconstraintsarethengovernedbyacombinationof ticl
r
lifetime and abundance, both being complementary with pa 10−1
respect to the vector mass: τ (Y ) decreases(increases)
V V
withlargerm . Fromthisoneexpectsconstraintsaslocal-
V
ized islands in those parameters where the epoch of pri-
mordialnucleosynthesisexhibitsitsgreatestsensitivity. 10
mV (GeV)
3.1 Majoreffectsandtreatment
Figure2. Pythiasimulationontheaveragenumberofparticles
TheeffectsonBBNareunderstoodbyconsideringelectro-
perV decayandontheinjectedelectromagneticenergyafterall
magnetic and hadronicenergy injection separately. Prior
particles havedecayed or annihilated toelectrons and photons.
to decay, the V abundancerelativeto baryonsis substan-
Aboutonethirdoftheenergyiscarriedawaybyneutrinos. Nar-
tial, nV/nb . 108 for τV < 1s, and the decays of V in- rowhadronicresonancesareneglected.
jectelectrons,muons,andmesonsinnumberslargerthan
baryons.
Darkphotondecayswith m 2m = 279MeVre-
V π
≤ ±
sultexclusivelyininjectionofelectromagneticenergy,be-
frommuondecayconstituteonlyminorcorrectionstothe
causeV e+e ,µ+µ aretheonlykinematicallyaccessi-
− −
→ photon-inducedprocesseslistedabove[5].
blemodes. Muonstypicallydecaybeforeinteracting,and
For vector masses abovethe di-pion threshold, m >
electron-positronpairsarequicklythermalizedbyinterac- V
2m ,hadronicmodesareaccessibleinthedecayofVand
tionswithbackgroundphotons.Theresultingelectromag- π±
theeffectsonBBNaremoreintricate. Inthehadronicde-
neticcascadewithspectrum f (E )entailsalargenumber
γ γ cay ofV onlyπ , K , and K , with lifetimesτ 10 8s,
ofnon-thermalphotonsthatmaythenspalllightelements. ± ± L ∼ −
and(anti-)nucleonshaveachancetoundergoastrongin-
Importantly,thespectrumhasarelativelysharpcut-off
teractionreactionbeforedecayingbythemselves.
for energiesabove the e pair-creationthreshold, E
± pair
m2/(22T). Photons with E > E are being dissipate≃d Before deuterium formation at T 100keV, only
e γ pair chargeexchangereactionsonnucleons,≃suchasπ + p
before they interact with nuclei, and to good approxima- −
→
π0+n,arepossible.Theychangethen/pratioandthereby
tion f (E ) = 0for E > E . Photonswith E < E ,
γ γ γ pair γ pair
mostprominentlytheprimordial4Hevalue.Afterthedeu-
however, undergoslower degradationprocesses and may
terium bottleneck—once light elements have formed—
interactwiththelightelementsbeforebeingthermalized.
charge exchange creates “extra neutrons” on top of the
EquatingE againstthephoto-destructionthresholds(in
pair
residual and declining neutron abundance. In addition,
brackets below) yields the temperature and thereby the
absorption with subsequent destruction of light elements
cosmictimet ofbiggestimpactforaspallationchannel:
ph
suchasπ +4He T +nisnowoperative.Spallationof
−
→
2 104s, 7Be+γ 3He+4He (1.59MeV), 4Hemayalsohaveasecondaryconsequence: theproduc-
× →
tph  5 104s, D+γ n+p (2.22MeV), tion of mass-3 elements with non-thermalkinetic energy
≃ 4××106s, 4He+→γ→3He/T+n/p (20MeV), may induce reactions of the sort T + 4Hebg → 6Li+ n.
The spallation rate of species N with numberdensity In the numericalanalysis, these processesaswell as sec-
ondarypopulationsofπ fromkaondecays,andhyperon
±
n isgivenby
N producing channels from reactions of kaons on nucleons
Emax and nuclei are being accounted for. Furthermore, in our
Γph(T)=2nN dEγ fγ(Eγ)σγ+N X(Eγ), (10) analysis, we restrict ourselves to reactions at threshold,
ZEthr → withchargedpionsandkaonsbeingthermalizedbeforere-
whereσ (E )isthephoto-dissociationcrosssection actingonlightelements;suchapproximationgenerallyre-
γ+N X γ
for γ + N → X with threshold E . The factor of two sultsinmoreconservativeconstraints.Adetailedquantita-
thr
→
accountsfor the two independentcascadesthatformin a tivediscussionofincompletestoppingcanbefoundin[5].
back-to-back decay of V at rest, each with a maximum Finally, baryonpairsare producedin the V-decayfor
energyof E = max E ,E /2 . All spallation reac- m & 2GeV. Final state nucleons n¯ and p¯ will prefer-
max pair inj V
tions listed in [14] arentaken into aoccount in the numer- entially annihilate on protons with an annihilation cross
ical analysis. We note in passing that neutrino injection section σ v m 2. Theinjectionofnn¯ thenresultsin
h ann i ∼ −π±
EPJWebofConferences
agreement with [17] when using a baryon asymmetry of
1 e± π± K± ηb =6.2 10−10andaneutronlifetimeofτn =885.7s.
Brem ×
ng 3.2 Lightelementobservations
hi
c
bran 10−1 µ± BofBlNighsetnesleitmiveitnytiasbautntadiannecdebsyanthdetohbeisreervsatitmioantaeldinefrerorrrebnacre.
e
tiv Here we briefly discuss those observations that form the
c p(p¯)
e basisofourobtainedregionsofinterest.
ff
e
d Themostabundantelementafterhydrogenishelium.
e
pt 10−2 n(n¯) ItsmassfractionYp isinferredfromextragalacticHIIre-
o
d gions,andvaluesintherange
a
0.24 Y 0.26 (11)
p
≤ ≤
10−3 havebeenreportedovertheyears.Owingtopotentialsys-
0.1 1
tematicuncertainties[18,19]weadopt(11)asthecosmo-
mV (GeV)
logicallyviablerange.
Amongrecentdevelopments,theprecisiondetermina-
Figure3. Finalstatebranchingratiosoflong-livedmesonsand
tionofD/Hfromhighredshiftquasarabsorptionsystems
otherrelevantdecayproducts.BaBarmeasurementsofthee
± → standsout[20,21]. Errorbarshavereducedbyafactorof
π ande K crosssectionsuptom = 1.8GeVarestiched
± ± → ± V fiveincomparisontopreviouslyavailabledeterminations.
together with a Pythia simulation starting at m 2.5GeV;
V ≥ Theweightedmeannowreads[21],
a branching to K was neglected and the fraction of m that
L V
is ultimately being converted to electromagnetic energy is la-
D/H=(2.53 0.04) 10 5. (12)
beledBr . −
em ± ×
D astration on dustgrainsis, however,a potentialsource
of systematic uncertainty,andvaluesas high as 4 10 5
−
×
havealsobeenreported[22,23]. Inlightofthis,weadopt
onenetp nconversionwithassociatedenergyinjection
→ anupperlimitof,
of m +m . Annihilation on neutronswith similar cross
p n
sectionisalsopossibleand pp¯ injectionresultsinonenet D/H<3 10 5. (13)
−
n p conversion. Assuming equal cross sections, the ×
→
relativeefficiencyis p/(n+p)andn/(n+p),respectively. as well. Finally, producingtoo little D/H yields a robust
At threshold, the rate for neutroninjection can be in- limitbecausenoknownastrophysicalsourcesofthisfrag-
ferred from a measurementof the e+e nn¯ cross sec- ilelightelementexist.Wethereforeeitherusethenominal
−
tion, σ 1nb [15]. Given a tota→l hadronic cross lower2σ-limitfrom(12)orrequire(robustly),
e+e nn¯
−→ ∼
section σ 50nb at this energy, the branching
e+e−→had ∼ 3He/D<1 (14)
fractiontoaneutron-antineutronpairis 2%. Awayfrom
∼
the di-nucleon threshold, with multi-pion(kaon) produc-
instead. Thelattervalueisderivedformsolarsystemob-
tion anddecaysto hyperonsandbaryonicresonancesbe-
servations[24].
ing prevalent, V-decays may be simulated using Pythia.
Finally, and with much smaller abundance, the pri-
The ultimate yield of π ,K , K , and nucleons prior to
± ± L mordial value of 7Li/H [25], is lower than the lithium
their decay is shown in Fig. 2; dots depict the average
yield from standard BBN by a factor of 3-5, 7Li/H =
electromagnetic energy that is injected after all particles
(5.24+0.71) 10 10[17].Weconsiderlithiumbeingincon-
have decayedto electronsandphotons; e+ have been an- 0.67 × −
corda−ncewithobservationsifBBNpredictionsyield
nihilated on e . The rest of the decay-energy is carried
−
away by neutrinos. At lower energies, decay events are 10 10 <7Li/H<2.5 10 10. (15)
− −
eventuallydominatedbytwobodydecays. Abovethedi- ×
pion(di-kaon)threshold,we use BaBar measurementsof Whilenewphysicsmaybeattheheartofthelithiumprob-
thee± π± ande± K± crosssectionuntilanreported lem, we caution thatastrophysicaldepletionmechanisms
→ →
energyof √s=mV =1.8GeV. Relevantultimatebranch- may also play their part in solution to this long-standing
ing ratios are shown in Fig. 3; the effects of KL are, for puzzle;see[26]forarecentreview.
simplicity,neglectedinourBBNanaslysis.
A moredetaileddiscussionalongwitha listofallin-
3.3 Results
cludedreactionscanbefoundintheoriginalpaper[7]as
wellasintheprecedingwork[5]. Numericalresultswere Our results from V-decays and their effect on BBN are
obtained by usage of a Boltzmann code that is based on presentedinthem ,κparameterspaceinFig.4. Contours
V
Ref. [16], with significant improvements and updates as ofconstantlifetime,τ andfreeze-inabundancen /n are
V V b
detailed in [5]. Standard BBN yields are found to be in shownbythediagonalsolidanddottedlines,respectively.
DarkMatter,HadronPhysicsandFusionPhysics
1100−−1100 4He followedby7Li+p→4He+4He.WithareducedCoulomb
2 II 3He/D barrier, 7Li is more susceptible to proton burning in the
1100−−1111 6 7LDi//HH secondstepandthedeclining7Litrendisdepictedbythe
6Li/H dashed lines in Fig. 4. Most of the extra neutrons, how-
logτV ever,endupbeingcapturedbyprotonsandtheassociated
1100−−1122 5 Ia logYV D/Hconstraint(13)isgivenbytheorangeregion.
III
3
κκ
1100−−1133 Ib 4 Conclusions
8
The kinetic mixing of a new U(1) gaugegroup with the
Ic ′
1100−−1144 0 Standard Model U(1) factors of hyperchargeand, below
the electroweak scale, of electromagnetism is one of the
fewportalstothehiddensectorwithrenormalizablecou-
1100−−1155 plings. The associated gauge boson V is often called a
11 110011 110022 110033 110044
mmVV((MMeeVV)) “darkphoton”andinthismanuscriptwehavereportedthe
cosmologicallimitsfromBBN astheyhavebeenderived
Figure4. Vector mass mV and kineticmixing parameter κ pa- in[7]. BBNsensitivityreachesphotonkineticmixingpa-
rameter space with BBN sensitivity. Diagonal gray contours rametersofκ 10 14for1MeV m .10GeV,unchal-
− V
depict τ (solid) or n /n prior to decay (dotted). Shaded re- ∼ ≤
V V b lengedfromterrestrialdarkphotonsearches,see, e.g.the
gionsareexcludedbyobservationsaslabeled.Thesolid(orange)
worksandpresentations[27–33]
closedlineisa2σconstraintfromunderproduction ofD/Hde-
The presented limits are based on a thermal abun-
rived from (12). Dashed black linesshow decreasing levels of
dance of V and a standard cosmological history of
7Li/H, 4 10 10 and 3 10 10, fromouter cirlcestotheinner
− −
ones,resp×ectively. Along×thedottedline6Li/H=10 12signify- the Universe—i.e.uneventfuluntilV-decay—withreheat
−
ingantwoordersmagnitudeenhanced6Liyield,thatis,however, temperaturesinexcessofmV. Additionalcontributionsto
notyetconstrainedbyobservations. theV-abundancesuchasfromaninitialV-condensateaf-
terinflationmayonlystrengthenthederivedbounds. The
latter source of primordial V-particles is particularly in-
teresting in the context of smaller V-masses. Below the
di-electronthreshold(notconsideredinthiswork),V has
TheregionslabeledI-IIIareinconflictwithobservations
anaturallylonglifetimewithV 3γbeingtheonlyde-
asdetailedintheprevioussection. →
cay mode. ThereforeV can evenbe a darkmatter candi-
InregionsI,Vdecaystoe+e resultinelectromagnetic
− date [6, 34] and ensuing constraints on the photoelectric
energyinjection.RegionIa(τ 105s)ismarkedbyade-
V ∼ absorption of V on atoms in dark matter detectors have
struction of 7Be and D. The 7Li/H abundanceis reduced
startedtoreceiveattentiononlyveryrecently[34–37].
to4 10 10 and3 10 10 fromtheoutsidetotheinside,
− −
× ×
respectively. However, cosmologically favored smaller
7Li/H abundances are challenged by3He/D < 1 (pink Acknowledgements
shaded region). Using (12), lower 7Li/H values are ex-
The speaker thanks S. Eidelman for the invitation to the
cludedbythenominal2σlowerlimitonD/Hasdepicted
workshop. JPissupportedbytheNewFrontiersprogram
bythesolidclosedline. RegionIbisadditionallymarked
bytheAustrianAcademyofSciences.
by spallation of 7Li and 7Be from non-thermal photons.
Thisresultsindirectproductionof6Li/H>10 12—values
−
yet too low for being observationally constrained at the References
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