1. 1 VIP Experiment (VIolation of the Pauli Exclusion Principle): a search for possible violation for electrons Laura Sperandio Laura Sperandio LNF - INFN LNF - INFN On behalf of the VIP Collaboration XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006 Frascati (Italy)

2. 2 Pauli exclusion principle The Pauli Exclusion Principle (PEP) represents one of the fundamental principles of the modern physics and our comprehension of the surrounding matter is based on it. Even if today there are no compelling reasons to doubt its validity, it still spurs a lively debate on its limits, especially for those theories related to possible PEP violation coming from new physics. There are several theoretical reasons to push the experimental limit in the region of 10 -30 : for example the validity of Pauli principle in a higher-dimensional space-time with small violation in the 3+1 known dimensions, or strings and superstrings etc. There are several theoretical reasons to push the experimental limit in the region of 10 -30 : for example the validity of Pauli principle in a higher-dimensional space-time with small violation in the 3+1 known dimensions, or strings and superstrings etc. “More recently … membrane theorists have been speculating on a large compactification radius for one of their eleven dimensions, which could give a ratio (for PEP violation) of 10 -30 ” [1] “More recently … membrane theorists have been speculating on a large compactification radius for one of their eleven dimensions, which could give a ratio (for PEP violation) of 10 -30 ” [1] [1]I. Duck and E. C. G. Sudarshan: Towards an understanding of the spin- statistics theorem, Am. J. Phys, 66 (1998) 284. [1]I. Duck and E. C. G. Sudarshan: Towards an understanding of the spin- statistics theorem, Am. J. Phys, 66 (1998) 284. XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

3. 3 The VIP experiment has the scientific goal of reducing by four orders of magnitude the limit on the probability of a possible violation of the Pauli exclusion principle for the electrons The VIP experiment has the scientific goal of reducing by four orders of magnitude the limit on the probability of a possible violation of the Pauli exclusion principle for the electrons Goal of VIP ( Ramberg & Snow -1990) from… …to XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

4. 4 The parameter  Ignatiev & Kuzmin model creation and destruction operators connect 3 states connect 3 states - the vacuum state - the vacuum state - the single occupancy state - the single occupancy state - the non-standard double occupancy state - the non-standard double occupancy state 0000 1111 2222 through the following relations: The parameter  quantifies the degree of violation in the transition. It is very small and for   0 we can have the Fermi -. It is very small and for   0 we can have the Fermi - Dirac statistic again.  1   2222 XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

5. 5 Normal 2p  1s transition 2p  1s transition violating Pauli principle Search for anomalous X-ray transitions Experimental method 8.05 keV in Cu~ 7.7 keV in Cu n=2 n=1 n=2 XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

6. 6 Evaluation of the anomalous X-ray energy in the copper We calculated the energy shift of the anomalous X-ray, with respect to the “normal” transitions, for three possible decay channels: - direct transition to 1s (K-edge) from the conduction band - 2p capture with a subsequent K  emission - 3p capture with a subsequent K β emission SUDDEN APPROXIMATION Transition time Orbital relax time (characteristic time of electronic transitions) electronic transitions) We used the XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

7. 7 The decay cross section, in the dipole approximation, is given by the “Fermi golden rule”:  E between the two levels Energy of the  Energy conservation Naturally: The K-edge case is the less probable the dipolar term is forbidden and the allowed quadrupolar term (3d  1s) is very small. The selection rule  ℓ=1 favours the 3d  2p and 2p  1s (or 3d  3p and 3p  1s) decays rather than the direct 3d  1s. XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006 Radiative process Radiative process

8. 8 Frozen-core approximation K a - transitions 2p  1s 3p  1s K  - transitions XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

9. 9 Frozen-core approximation K-edge decays 3d  1s The uncertainty on these values is around some tens of eV. “Evaluation of the anomalous X-ray energy in VIP experiment”, VIP Note-IR-03 (March, 2005) “Evaluation of the anomalous X-ray energy in VIP experiment, some values”, VIP Note-IR-04 (April, 2005) “Background measurement with a 2 CCD test setup for the VIP Experiment”, VIP Note-IR-05 (April, 2005) XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

10. 10 Dirac-Fock multiconfiguration method Software for muonic atoms non-antisymmetrized e - !!! It takes into consideration: - relativistic corrections - lamb-shift - lamb-shift - Breit operator - Breit operator - radiative corrections - radiative corrections Self-consistent method for the optimization of the parameters XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

11. 11 Transition energies of the anomalous X-rays in Copper Paul Indelicato (Ecole Normale Supérieure et Université Pierre et Marie Curie) Multiconfiguration Dirac-Fock approach core: (1s)2(2s)2(3s)2(2p*)2(3p*)2(2p)4(3p)4(3d*)4(3d) Transition Initial en. Final en. Transition Radiative transition Multipole order energy rate (s-1) 2p 1/2 - 1s 1/2 -45799 -53528 7729 2.63E+14 E1 2p 3/2 - 1s 1/2 -45780 -53528 7748 2.56E+14 E1+M2 3p 1/2 - 1s 1/2 -44998 -53528 8530 2.78E+13 E1 3p 3/2 - 1s 1/2 -44996 -53528 8532 2.68E+13 E1+M2 Normal copper: ~ 8040 eV (2p  1s) Note: similar value obtained by S. Di Matteo e L. Sperandio in the “sudden approximation”. KK KβKβ XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

12. 12 Transition energies of the anomalous X-rays in Copper Paul Indelicato (Ecole Normale Supérieure et Université Pierre et Marie Curie) Multiconfiguration Dirac-Fock approach core: (1s)2(2s)2(3s)2(2p*)2(3p*)2(2p)4(3p)4(3d*)4(3d) Transition Initial en. Final en. Transition Radiative transition Multipole order energy rate (s-1) 2p 1/2 - 1s 1/2 -45799 -53528 7729 2.63E+14 E1 2p 3/2 - 1s 1/2 -45780 -53528 7748 2.56E+14 E1+M2 3p 1/2 - 1s 1/2 -44998 -53528 8530 2.78E+13 E1 3p 3/2 - 1s 1/2 -44996 -53528 8532 2.68E+13 E1+M2 Normal copper: ~ 8040 eV (2p  1s) Note: similar value obtained by S. Di Matteo e L. Sperandio in the “sudden approximation”. KK KβKβ XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

13. 13 Results and discussion  [ΔE DF (K α ) – ΔE(K α )] / ΔE DF (K α )  ≈ 9.95 ∙ 10 -3 ≈ 1 %  [ΔE DF (K b ) – ΔE(K b )] / ΔE DF (K b )  ≈ 0.010 ≈ 1 % From radiative transition rates K  transition is 10 times more probable than K β one 3) 1) 2) K-edge decay is not a purely atomic process its transition rate cannot be estimated with the DF-code Through a weighted average ΔE DF (K α ) = 7742 eV ΔE DF (K β ) = 8531 eV XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

14. 14 But... why? All these calculations have the goal to determine the “region of interest” where VIP has to look for the anomalous X-rays generated by the PEP violation by electrons their precision reduces the systematic errors. First results of this experiment: see talk by D. Sirghi. XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

15. 15 This brings up an interesting question: Why is it that particles with half-integral spin are Fermi particles (...) whereas particles with integral spin are Bose particles (...)? We apologize for the fact that we can not give you an elementary explanation. An explanation has been worked out by Pauli from complicated arguments from quantum field theory and relativity. He has shown that the two must necessarily go together, but we have not been able to find a way to reproduce his arguments on an elementary level. It appears to be one of the few places in physics where there is a rule which can be stated very simply, but for which no one has found a simple and easy explanation. (...) This probably means that we do not have a complete understanding of the fundamental principle involved. For the moment, you will just have to take it as one of the rules of the world Feynman Lectures on Physics XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

16. 16 O.W. Greenberg: AIP Conf.Proc.545:113-127,2004 “Possible external motivations for violation of statistics include: (a) violation of CPT, (b) violation of locality, (c) violation of Lorentz invariance, (d) extra space dimensions, (e) discrete space and/or time and (f) noncommutative spacetime. Of these (a) seems unlikely because the quon theory which obeys CPT allows violations, (b) seems likely because if locality is satisfied we can prove the spin- statistics connection and there will be no violations, (c), (d), (e) and (f) seem possible………….. Hopefully either violation will be found experimentally or our theoretical efforts will lead to understanding of why only Bose and Fermi statistics occur in Nature.” Theories of Violation of Statistics XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006

17. 17 Dirac-Fock method Self-consistent method for the optimization of the parameters No-pair approximation Corrections (Breit operator, Lamb shift, radiative corrections) Previously used for muonic atoms Breit operator Coulomb interaction XI FRASCATI SPRING SCHOOL “BRUNO TOUSCHEK” LNF, May 15th – 19th, 2006