# Presentation: 570568

## 3+2 Neutrino Phenomenology and Studies at MiniBooNE

**PHENO 2007 Symposium**
- May 7-9, 2007
- U. Wisconsin, Madison

**Georgia Karagiorgi, Columbia University**

## Outline

- Motivation for 3+2 models
- 3+2 phenomenology and oscillation formalism
- The MiniBooNE result and experimental constraints for 3+2 models
- CP violation studies in 3+2 models and prospects for CPV measurement at MiniBooNE
- Current status of 3+2 analysis and future plans
- Conclusions

- G. Karagiorgi *et al*., “Leptonic CP violation studies at MiniBooNE in a (3+2) sterile neutrino oscillation hypothesis,” Phys. Rev. D. **75**, 013011 (2007) [hep-ph/0609177].

- Georgia Karagiorgi, Columbia U.

## The LSND Signal

**Δ****m****2****LSND**** >> ****Δ****m****2****atm**** ****>>**** Δ****m****2****sol**
**        **

**Δ****m****2****LSND**** ~ 0.1- 10 eV****2****  +  small mixing**

******one option:** **3 active + n “sterile” neutrinos******other options: neutrino decay, extra-D, etc.

- Georgia Karagiorgi, Columbia U.

**Notes:**
3+n sterile is more attractive because it requires minimal extensions beyond the SM 

## 3+2 Model Phenomenology

- 3 active + 2 **sterile** neutrinos

*** ******light**** *sterile neutrinos
-  they can interact thru non-standard weak couplings
-  they have very small active flavor content (Ue4,..., Ue5,...)
- 	 can participate in neutrino oscillations

- νe
- νμ
- ντ
- νs

- increasing m2(not to scale)

*Why n=2? *
*3+1 models: SBL and LSND marginally consistent with each other *
*3+2: next natural step...**	**	**	**[M. Sorel, et al. hep-ph/0305255]*

- Georgia Karagiorgi, Columbia U.

## 3+2 Model Phenomenology

**GUT’s**
- 	Mohapatra, Nasri, & Yu **[*****hep-ph/0505021*****]**
*	*De Gouvea, Jenkins, & Vasudevan **[*****hep-ph/0608147*****]**
**Extra-D**
- 	Pas, Pakvasa, & Weiler **[*****hep-ph/0504096*****]**
* **	*Ma, Rajasekaran, & Sarkar **[*****hep-ph/0006340*****]**
**SUSY**
- 	Kang, & Li **[*****hep-ph/0501101*****]*** *
- 	Dvali, & Nirb **[*****hep-ph/9810257*****]**

- Georgia Karagiorgi, Columbia U.

## 3+2 Neutrino Oscillation Formalism

- General neutrino oscillation formula:
*P(**ν**α**** **ν**β**) = δ**αβ** – 4** *Σ*Re *(*U***α**i**U**β**i**U**α**j**U***β**j*) *sin**2**x**ij** *
*	**	**           **+ 2 *Σ*Im *(*U***α**i**U**β**i**U**α**j**U***β**j*) *sin2x**ij*
***P(******ν******μ************ ******ν******e******) = ******4******|******U******μ4******|******2******|******U******e4******|******2******sin******2******x******41****** + 4******|******U******μ******5******|******2******|******U******e5******|******2******sin******2******x******51****** +***
***	******	******	******        ******+ 8 ******|******U******μ******5******||******U******e5******|******|******U******μ4******||******U******e4******|sinx******41******sinx******51******cos(x******54******+******φ******45******)***

**Assumptions for 3+2 model analysis:**
- approximate** *****m******1****** = m******2****** = m******3****** = 0***** *        **
- two independent mass splittings:** *****Δ******m******2******41***,*** ******Δ******m******2******51***** **
- four moduli:** *****|U******e4******|****,**** ******|U******μ******4******|****,**** ******|U******e******5******|****,**** ******|U******μ5******|***
- one CPV phase:** *****φ******54****** = arg(U*************μ5 ******U******e******5 ******U******μ******4 ******U*************e4******)***

*** This allows for 6 ******** 1 CPV phase in a (3+2) hypothesis**
**	****      ****(3 ******** 0 CPV phases in a (3+1) hypothesis)**
**	****      ****(1 ******** 0 CPV phases in a (3+0) hypothesis)**
***	******3+2 model = most minimal model***
***	******	****** ******for CPV studies!***

*x**ij**  = 1.27**Δ**m**2**ij** L/E*

- Georgia Karagiorgi, Columbia U.

## First Results from MiniBooNE

- “A Search for Electron Neutrino Appearance at the Δm2 ~ 1eV2 Scale,” The MiniBooNE Collaboration [hep-ex/0704.1500].

- MiniBooNE result **excludes** the LSND 90%CL allowed region**at > 90% CL**...

- Georgia Karagiorgi, Columbia U.

## First Results from MiniBooNE

- ...MiniBooNE result assumes:
- 	**CP-conserving, 2-neutrino oscillation scenario**
**	****E > 475 MeV**
**Excess of ****ν****e**** events at low energies:**
- 	Currently investigating if this is a detector effect, or SM background...
- 	Could be a manifestation of beyond the SM physics...

*For more information on this, see talk by Chris Polly*

- Georgia Karagiorgi, Columbia U.

## Experimental Constraints

- We are interested in:
- studying the **compatibility **of null SBL results with LSND and MiniBooNE results in a 3 active + 2 sterile neutrino hypothesis
**constraining the** **3+2 model parameters**

| 
Channel | 
Experiment | 

Lowest Δm2 Reach (90%CL) | 

High Δm2 | 

Optimal Δm2 |
| --- | --- | --- | --- | --- |
| νμ  νe | LSNDKARMENNOMADMiniBooNE | 3x10-26x10-24x10-12.5x10-2 | > 2.5x10-3< 1.7x10-3< 1.4x10-3 | > 1.2x10-3< 1.0x10-3 < 1.0x10-3 |
| νe  νe | BugeyChooz | 1x10-2
7x10-4 | < 1.4x10-1< 1.0x10-1 | < 1.3x10-2 < 5x10-2 |
| νμ  νμ | CCFR84CDHS | 6x100
3x10-1 | nonenone | < 2x10-1 < 5.3x10-1 |

**sin****2****θ**** constraint (90%CL)**

- Georgia Karagiorgi, Columbia U.

## Combined NSBL+LSND+MiniBooNE 

- 3+2 analysis (including MB νe* *background disappearance)
- and compatibility tests are currently **in progress**...
- Recent studies:
*Leptonic CP violation studies at MiniBooNE in a 3+2 sterile neutrino oscillation hypothesis*
-  Expected oscillation probability at MiniBooNE
-  Potential of CP-violation measurement at MiniBooNE

***[hep-ph/0609177]***

*Dataset: NSBL + LSND only (no atmospheric or solar experiment data) **+ Super-K atm. constraint*

- Georgia Karagiorgi, Columbia U.

## Oscillation Analysis for CPV Studies at MiniBooNE

- Generate masses and mixing parameters (models):
*0.1eV**2** **≤** **Δ**m**2**41**,   **Δ**m**2**51** **≤ 100eV**2*
*	**Δ**m**2**51 **≥** **Δ**m**2**41*
*|U**e4**|, |U**μ**4**|,** **|U**e**5**|,** **|U**μ5**|*
*	**U**ei**2** + U**μ**i**2** **≤ 0.5**, * *U**α**4**2** + U**α5**2** **≤ 0.5*
*atmospheric constraint:**	** **d**μ** = *1⁄2 - √(1-4*A)** **/2*
*	**where **A = (1 - |U**μ*4|2 - |*U**μ*5|2)(|*U**μ*4|2 + |*U**μ*5|2) + |*U**μ*4|2|*U**μ*5|2
*	**CP violation option: Fix **φ**54** **=** **0,** **π**,** or allow to vary within **(0,2**π)*
- Calculate expected oscillation probabilities in neutrino and anti-neutrino running mode
- 	at MiniBooNE
- 	(using expected full νμ  νe transmutation rates)
- Determine allowed regions by Gaussian approximation

- Importance sampling via Markov chain:
*P*(*x**i**** x**i+1*)* = min*{*1,exp*[*-*(*χ**2**i+1**-**χ**2**ι*)*/Τ*]}
*x**i+1** = x**i** + e*

***P(******ν******μ************ ******ν******e******) = ******4******|******U******μ4******|******2******|******U******e4******|******2******sin******2******x******41****** + 4******|******U******μ******5******|******2******|******U******e5******|******2******sin******2******x******51****** +***
***	******	******	******        ******+ 8 ******|******U******μ******5******||******U******e5******|******|******U******μ4******||******U******e4******|sinx******41******sinx******51******cos(x******54******+******φ******45******)***

- Georgia Karagiorgi, Columbia U.

## Oscillation probability expected at MiniBooNE

- Oscillation probability expected at MiniBooNE

- CP-violating 3+2 models

- CP-conserving 3+2 models

**90%CL ****99%CL**

- Best fit models:CPC: *χ**2**/dof* = 141.4/145CPV: *χ**2**/dof* = 140.8/144

- Georgia Karagiorgi, Columbia U.

## Potential observation of CP-violation at MiniBooNE

***All CP-violating phase values allowed at 99%CL by the NSBL+LSND data are measurable at MiniBooNE***

- Small degrees of CPV preferred
- Large asymmetries allowed, but not required

**90%CL ****99%CL**

- Georgia Karagiorgi, Columbia U.

## First global fit results

***Analysis by Maltoni & Schwetz******Fig. 7 [hep-ph/0705.0107]***

**Best fit parameters for global fit with full MiniBooNE E range:**
*Δ**m**2**41* = 0.87eV2		*x**2**min **/dof *= 104.4/(109-7)
*Δ**m**2**51* = 1.91eV2		*gof *= 41%
*cpv-phase* = 1.44π

*χ**2**PG** = 17.5 , PG = 1.5**x**10**−3** (no MB)*
*χ**2**PG** = 25.1 , PG = 4.8**x**10**−5** (MB300)*

- Georgia Karagiorgi, Columbia U.

## Potential observation of CP-violation at MiniBooNE

- MiniBooNE expected oscillation probability asymmetry
****** ****based on calculated best fit model parameters from hep-ph/0705.0107 global 3+2 analysis (****MB300 ****and ****MB475****)**

**MB300**
***A******p/p****** = -0.448***
***φ******45****** = 1.44******π***

**MB475**
***A******p/p****** = -0.207***
***φ******45****** = 1.64******π***

- Georgia Karagiorgi, Columbia U.

## First global fit results

***Maltoni & Schwetz******Fig. 3 [hep-ph/0705.0107]***

- MB signal prediction from best fit points from SBL appearance data (LSND, KARMEN, NOMAD, MB) in a 3+2 oscillation analysis

- 3+2 neutrino models:
-  provide a **good fit** to LSND and the recent MB data
-  can **account for the low energy** event **excess in MB**
- However:
-  there is significant **tension** **between appearance and disappearance data** (according to the PG test at the level of 3σ for MB475 and 4σ for MB300).

***Note: analysis done without full MiniBooNE error matrix***

- Georgia Karagiorgi, Columbia U.

## Our next 3+2 steps...

- More detailed combined NSBL + LSND + MiniBooNE
- 	3+2 oscillation analysis and compatibility tests, that take into consideration:
- Full MiniBooNE error matrix
- Disappearance of MiniBooNE νe background

- Georgia Karagiorgi, Columbia U.

## Conclusions

- Original motivation: accommodate null SBL and LSND results within the framework of neutrino oscillations
- MiniBooNE data: key in addressing the viability of 3+2 models with sterile neutrinos
- Leptonic CP-violation possibility opened up in the 3+2 sterile neutrino hypothesis could have large measurable effects at MiniBooNE

- Georgia Karagiorgi, Columbia U.