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& DBD GERDA Calibration System Outlook

The Calibration System for the GerdaExperiment

Francis Froborg

Universitat Zurich

Doktorandenseminar30. August 2010

Francis Froborg Calibration of Gerda

& DBD GERDA Calibration System Outlook

Neutrino Physics

We know

Neutrinos have a mass

Mass difference betweeneigenstates

Three big questions

Absolute mass scale

Mass hierarchy

Majorana vs. Dirac

Francis Froborg Calibration of Gerda

& DBD GERDA Calibration System Outlook

Double Beta Decay

2

(Z ,A) (Z + 2,A) + 2e + 2e

L = 0T 2

1/2

1= G2(Q ,Z) |M2 |2

1020 y

1

3

!"

"

n

n p

p

e

e

!

W

W

"#

n

n p

p

e

eW

W

x

FIG. 2 Feynman Diagrams for (2) (left) and (0)(right).

where G0(Q , Z) is the phase space factor for the emis-sion of the two electrons, M0 is another nuclear matrixelement, and m is the effective Majorana mass ofthe electron neutrino:

m |

k

mkU2ek| . (3)

Here the mks are the masses of the three light neutrinosand U is the matrix that transforms states with well-defined mass into states with well-defined flavor (e.g.,electron, mu, tau). Equation 2 gives the (0) rateif the exchange of light Majorana neutrinos with lefthanded interactions is responsible. Other mechanismsare possible (see Sections III and IV.D), but they requirethe existence of new particles and/or interactions in ad-dition to requiring that neutrinos be Majorana particles.Light-neutrino exchange is therefore, in some sense, theminima mechanism and the most commonly consid-ered.

That neutrinos mix and have mass is now acceptedwisdom. Oscillation experiments constrain U fairly well

Table I summarizes our current knowledge but theydetermine only the differences between the squares of themasses mk (e.g., m22 m21) rather than the masses them-selves. It will turn out that (0) is among the bestways of getting at the masses (along with cosmology and-decay measurements), and the only practical way toestablish that neutrinos are Majorana particles.

To extract the effective mass from a measurement, itis customary to define a nuclear structure factor FN G0(Q , Z)|M0 |2m2e, where me is the electron mass.(The quantity FN is sometimes written as Cmm.) Theeffective mass m can be written in terms of the cal-culated FN and the measured half life as

m = me[FNT 01/2]1/2 . (4)

The range of mixing matrix values given below in Ta-ble I, combined with calculated values for FN , allow usto estimate the half-life a given experiment must be ableto measure in order to be sensitive to a particular valueof m. Published values of FN are typically between1013 and 1014 y1. To reach a sensitivity of m0.1 eV, therefore, an experiment must be able to observea half life of 1026 1027 y. As we discuss later, at thislevel of sensitivity an experiment can draw importantconclusions whether or not the decay is observed.

The most sensitive limits thus far are from theHeidelberg-Moscow experiment: T 01/2(

76Ge) 1.9 1025 y (Baudis et al., 1999), the IGEX experiment:T 01/2(

76Ge) 1.6 1025 y (Aalseth et al., 2002a, 2004),and the CUORICINO experiment T 01/2(

130Te) 3.0 1024 y (Arnaboldi et al., 2005, 2007). These experimentscontained 5 to 10 kg of the parent isotope and ran forseveral years. Hence, increasing the half-life sensitivityby a factor of about 100, the goal of the next generationof experiments, will require hundreds of kg of parent iso-tope and a significant decrease in background beyond thepresent state of the art (roughly 0.1 counts/(keV kg y).

It is straightforward to derive an approximate an-alytical expression for the half-life to which an ex-periment with a given level of background is sensi-tive (Avignone et al., 2005):

T 01/2(n) =4.16 1026y

n

( a

W

)

Mt

b(E). (5)

Here n is the number of standard deviations correspond-ing to a given confidence level (C.L.) a CL of 99.73%corresponds to n = 3 the quantity is the event-detection and identification efficiency, a is the isotopicabundance, W is the molecular weight of the source ma-terial, and M is the total mass of the source. The in-strumental spectral-width (E), defining the signal re-gion, is related to the energy resolution at the energyof the expected (0) peak, and b is the specific back-ground rate in counts/(keV kg y), where the mass is that

0

(Z ,A) (Z + 2,A) + 2e

L = 2T 0

1/2

1= G0(Q ,Z) |M0 |2 m2

1025 y

1m =

Pi

U2ei mi

3

!"

"

n

n p

p

e

e

!

W

W

"#

n

n p

p

e

eW

W

x

FIG. 2 Feynman Diagrams for (2) (left) and (0)(right).

where G0(Q , Z) is the phase space factor for the emis-sion of the two electrons, M0 is another nuclear matrixelement, and m is the effective Majorana mass ofthe electron neutrino:

m |

k

mkU2ek| . (3)

Here the mks are the masses of the three light neutrinosand U is the matrix that transforms states with well-defined mass into states with well-defined flavor (e.g.,electron, mu, tau). Equation 2 gives the (0) rateif the exchange of light Majorana neutrinos with lefthanded interactions is responsible. Other mechanismsare possible (see Sections III and IV.D), but they requirethe existence of new particles and/or interactions in ad-dition to requiring that neutrinos be Majorana particles.Light-neutrino exchange is therefore, in some sense, theminima mechanism and the most commonly consid-ered.

That neutrinos mix and have mass is now acceptedwisdom. Oscillation experiments constrain U fairly well

Table I summarizes our current knowledge but theydetermine only the differences between the squares of themasses mk (e.g., m22 m21) rather than the masses them-selves. It will turn out that (0) is among the bestways of getting at the masses (along with cosmology and-decay measurements), and the only practical way toestablish that neutrinos are Majorana particles.

To extract the effective mass from a measurement, itis customary to define a nuclear structure factor FN G0(Q , Z)|M0 |2m2e, where me is the electron mass.(The quantity FN is sometimes written as Cmm.) Theeffective mass m can be written in terms of the cal-culated FN and the measured half life as

m = me[FNT 01/2]1/2 . (4)

The range of mixing matrix values given below in Ta-ble I, combined with calculated values for FN , allow usto estimate the half-life a given experiment must be ableto measure in order to be sensitive to a particular valueof m. Published values of FN are typically between1013 and 1014 y1. To reach a sensitivity of m0.1 eV, therefore, an experiment must be able to observea half life of 1026 1027 y. As we discuss later, at thislevel of sensitivity an experiment can draw importantconclusions whether or not the decay is observed.

The most sensitive limits thus far are from theHeidelberg-Moscow experiment: T 01/2(

76Ge) 1.9 1025 y (Baudis et al., 1999), the IGEX experiment:T 01/2(

76Ge) 1.6 1025 y (Aalseth et al., 2002a, 2004),and the CUORICINO experiment T 01/2(

130Te) 3.0 1024 y (Arnaboldi et al., 2005, 2007). These experimentscontained 5 to 10 kg of the parent isotope and ran forseveral years. Hence, increasing the half-life sensitivityby a factor of about 100, the goal of the next generationof experiments, will require hundreds of kg of parent iso-tope and a significant decrease in background beyond thepresent state of the art (roughly 0.1 counts/(keV kg y).

It is straightforward to derive an approximate an-alytical expression for the half-life to which an ex-periment with a given level of background is sensi-tive (Avignone et al., 2005):

T 01/2(n) =4.16 1026y

n

( a

W

)

Mt

b(E). (5)

Here n is the number of standard deviations correspond-ing to a given confidence level (C.L.) a CL of 99.73%corresponds to n = 3 the quantity is the event-detection and identification efficiency, a is the isotopicabundance, W is the molecular weight of the source ma-terial, and M is the total mass of the source. The in-strumental spectral-width (E), defining the signal re-gion, is related to the energy resolution at the energyof the expected (0) peak, and b is the specific back-ground rate in counts/(keV kg y), where the mass is that

Francis Froborg Calibration of Gerda

& DBD GERDA Calibration System Outlook

Signature

Measuring the energy of both electrons

2: Continuous energy spectrum

0: Sharp peak at Q value of decay

Q = Emother Edaugther 2me

Schechter & Valle (1982): Measuring 0 Majorana particle

Francis Froborg Calibration of Gerda

& DBD GERDA Calibration System Outlook

Heidelberg-Moscow ExperimentThe Claim

5 HPGe crystals with 71.7 kg y

Peak at Q value:

T 01/2 = 1.2 1025y (4)

m = 0.44 eV

Problem: Confidence depends on backgroundmodel and energy region selectedfor analysis

New experiments with higher sensitivityneeded

Evidenz fr den Neutrinolosen Doppelbetazerfall?

Peak beim Q-Wert des Zerfalls

Periode 1990-2003: 28.8 6.9 Ereignisse

Periode 1995-2003: 23.0 5.7 Ereignisse

! 4.1- 4.2 ! Evidenz

Evidenz unklar

! muss mit neuen, empfindlicheren Experimenten getestet werden

T1/2

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