Resolving the axial mass anomaly

Neutrino Quasielas.c Sca1ering on Nuclear Targets Resolving the axial mass anomaly Eur.Phys.J.C71:1726,2011 arxiv:1106.0340 [hep- ph] Arie Bodek University of Rochester MIAMI 2011 Conference, Ft. Lauderdale, FL Friday, Dec. 16, 2011 2:30-3:00 pm A. Bodek 1

dσ/dq 2 G. Zeller 2011. Low Energy neutrino experiments (< 1.5 GeV) favor M A ~ 1.2-1.3 much larger than M A for free nucleons of 1.014 World average of all High Energy neutrino experiments on nuclear targets favors small M A Axial Mass anomaly A. Bodek

BBBA World Average Axial Form Factor measurements on Hydrogen and deuterium A. Bodek 3

(= Probelm Axial Mass anomaly: 30% Low energy cross sec.ons on nuclear targets are 20% high, consistent with: M A =1.35 CURVES: INDEPENDENT NUCLEON MODEL High energy experiments on nuclear targets are consistent with : M A =1.03 (= free nucleon value) difference in high energy cross sec.on is 30%. hia. Bodek 4

Axial Mass Anomaly Structure funcaons can depend only on Q 2 and ν Therefore, they must be the same at low and high energies (even for nuclear targets) A fundamental principle of lepton scadering. So which is right? Is it a difference in the experimental event selecaon process or modeling of acceptance between the low and high energy experiments of order 30%? Or is it something new? Note: There are theoreacal arguments that the axial form factor for bound nucleons should be the same as or smaller than for free nucleons- NOT LARGER > large M A in nuclei not expected theoreacally. A. Bodek 5

What do we learn from electron scadering data on nuclear targets. T. W. Donnelly and I. Sick, Phys. Rev. C60, 065502 (1999) 1. Model of Independent nucleon with Fermi moaon and free nucleon form factors works for the longitudinal part of the QE cross secaons 2. The transverse part of the QE cross secaons shows an excess which is Q 2 dependent 3. This was known for over a decade. A. Bodek 6

Electron QE scadering: Q 2 =0.09 GeV2 Q 2 =0.14 GeV2 Q 2-0.33 GeV2 Longitudinal Response Funcaon Longitudinal response funcaon in QE electron scadering (assume free nucleon form factors, and remove their contribuaon). What is lek is the response funcaon (Fermi momentum, or spectral funcaon) It is universal for A>12. and does not depend on momentum transfer. This is expected for independent nucleons. INDEPENDENT NUCLEON MODEL WORKS (WITH FREE NUCLEON FORM FACTORS) Donnely and Sick q =q3 = 3- momentum transfer No pion Producaon, Delta is mostly transverse QE peak 0.5 1.2 Above QE peak A. Bodek Between QE peak and Delta 7

Donnely and Sick Response func.ons (assume free nucleon form factors, and remove their Q2 dependence) Transverse is enhanced by a Q 2 factor R T Use this as the shape of the universal response funcaon Integrate A. Bodek Integrate 0.5 1.2 8

Carlson et al. PRC 65:024003 (2002) Q 2 =0.14 GeV2 Weak dependence on A for A>12 Q 2-0.33 GeV2 R T = Raao of Integrated Transverse to Longitudinal response funcaons (same as raao of transverse to independent nucleons). R T Q 2 =0.09 GeV2 Use difference between 1.2 and 0.5 as sys. error Use Carslon et al. extracted R T for Carbon and Calcium at: Q 2 =0.09 GeV2 Q 2 =0.14 GeV2 Q 2-0.33 GeV2 To get R T at higher Q 2 we use another method. A. Bodek 9

PRC 65:024003 (2002) Q 2 =0.09 GeV2 Q 2 =0.14 GeV2 Q 2-0.33 GeV2 Another method: Use Bosted- Mamyan fit to electron scadering e- A data ) There is no transverse enhancement at high Q 2 Q 2 GeV2 Use Carlson integrated excess : Raao R T (raao to universal response funcaon) Correct It for for high side tail A. Bodek 10

Extracang transverse enhancement at higher Q 2 (> 0.3 GeV 2 ) from e- A data In electron scadering, the QE cross secaon is dominated by Longitudinal part at low Q 2 and Transverse part at high Q 2. Therefore, at low Q 2 we need to separate L and T to get the Trans. Enhancement (since the cross secaon is mostly longitudinal). QE and Δ(1232) producaon are well separated at low Q 2. Pauli blocking mostly cancels in raao of T and L. At high Q 2, L is small, so it cannot be used as a normalizaaon. Here Trans. Enhancement is the raao of the measured cross secaon to the predicaon of the independent nucleon model - Here we need to separate QE from Δ(1232) producaon (with Fermi moaon). At high Q 2, Pauli blocking is negligible. A. Bodek 11

Electron scadering data on Nuclear targets JUPITER collaboraaon (E04-001) at Jlab (e- A). Focus on invesagaaon of electron scadering on nuclear targets, with emphasis on measuring L and T vector structure funcaons in the QE and Resonance region, for Q 2 values of interest to neutrino scadering experiments Collaborate with Neutrino Oscillaaons experimenters (e.g. MINERvA, T2K). E04-001 Spokespersons: A. Bodek, C. Keppel, M. E. Christy. Details in: Measurements of F2 and R = σ L /σ T on Nuclear Targets in the Nucleon Resonance Region by Mamyan, Vahe, Ph.D., UNIVERSITY OF VIRGINIA, 2010 A. Bodek 12

In order to do the radiaave correcaons to e- A data, we do a fit to electron scadering data from many experiments over a large range of energies and Q2. The fit includes the following three components QE Longitudinal QE transverse QE TE Inelas.c calculaaon includes Pauli Blocking. Fit developed by Peter Bosted and tuned by Vahe Mamyan for E04-001 It uses fits to all experimental data on H and D, (by Bosted and Christy) As input for fisng the data on nuclear targets. For QE super- scaling model of Sick, Donnelly, Maieron (nucl- th/ 0109032) is used. A. Bodek 13

Bosted- Mamyan fit Extracang Transverse enhancement at Q 2 >0.3 GeV2 In order to fit the data on nuclear targets we find that a TE component is needed. We take the TE component from the fit, Integrate up to W 2 = 1.5, and extract R T ( Q2 )= ( QE trans + TE )/QE trans Assign a conservaave systemaac error to R T (since some of the transverse excess may be produced with final state pions) (In future we plan to improve it with updated L- T separated data from E04-001) Primary purpose of this preliminary fit was as input to radiaave correcaons. Q2=0.68 Total QE TE QE Long QE trans Inelas.c A spinoff of the fit is the TE component versus Q2 A. Bodek 14

Q2=0.3 Q2=1.0 Q2=0.68 Q2=1.1 A. Bodek 15

Transverse Enhancement has been adributed to Meson Exchange Currents MEC enhance only the transverse part of the QE cross secaon. MEC do not enhance the longitudinal part, or the axial part. By Conserved Vector Current (CVC), the transverse enhancement observed in electron scadering experiments should be seen in neutrino scadering. THEREFORE: We parametrize the observed transverse enhancement in electron scadering as an enhancement in the magneac form factors GMp and GMn for bound nucleons (magneac scadering is transverse). (This is simple to implement in current neutrino MCs ) And predict neutrino QE diff and total cross secaons using the independent nucleon model with free nucleon form factors (except for Gmp and Gmn which are enhanced). Integrated over ν We do not need a detailed specific model of MEC. - - Just CVC, so this is valid even if TE is not MEC (e.g. it can be any nuclear physics correcaon to the transverse cross secaon) A. Bodek 16

Most of the cross secaon is a lower Q2. Larger errors at large Q2 A. Bodek 17

Predicaons: Low energy Carbon (~1 GeV) At low energies: dσ/dq 2 Q 2 range is limited ( 0< Q 2 < 1.3 GeV 2 ) transverse enhancement looks similar to M A =1.30 Independent nucleons with M A =1.014 Q 2 max = 1.3 Most of the cross secaon is low Q2 All predicaons include Pauli Blocking. >>> MA is not large in nuclear targets A. Bodek 18

Lower energies have lower Q 2 max, where the transverse enhancement is large. Large difference in Q 2 max between E=1 GeV and E= 3 GeV neutrino energies Q 2 max = 4.9 for E= 3 GeV Q 2 max = 1.3 for E= 1 GeV A. Bodek 19

) 2 cm 2 /(GeV/c) -38 (10 2 d /dq 2 1.8 1.6 1.4 1.2 1 0.8 0.6 2 - d /dq, + n p +!, E =3 GeV M A =1.014 M A =1.30 V Tranv Enhance in G M, M A =1.014 Need E>2 GeV to access Q2 above 1 GeV2, High energy experiments put a Q 2 cut to fit data in a region where there is no Pauli Blocking. At high Q 2 transverse enhancement looks Like M A <1.014 since dσ/dq 2 transiaons between M A =1.30 curve and M A =1.014 curve, so it is steeper than M A =1.014. free nucleons 0.4 0.2 0 0 0.5 1 1.5 2 2.5 All predicaons include Pauli Blocking. 2 2 Q (GeV/c) World average of all High energy neutrino experiments on nuclear targets is A. Bodek 20

( 10-38 cm 2 ) 1.6 1.4 1.2 1 0.8 Total QE cross secaons on Carbon (per neutron) M A =1.014 + n p +! - MiniBooNE, C Nomad, C Martini et al. E<1.2 GeV MEC model M A =1.30 transverse enhancement Note: NOMAD needs to 0.6 Mar.ni et al E<1.2 GeV MEC model include TE in modeling the PRC 81: 045502 (2010) acceptance/efficiency 0.4 correcaons for stringent cuts used to reduce background 0.2 M A =1.014 Independent Nucleon model M A =1.30 Large M A independent nucleon model V Tranv Enhance in G M, M A =1.014 0-1 2 10 1 A. Bodek 10 21 10 All predicaons include Pauli Blocking. E (GeV)

Changing GM in the neutrino Monte Carlo as a way to parametrize TE is a good way to approximate the TOTAL integrated TE contribuaon on AVERAGE, and a first order descripaon of the Q2 dependence. This is a good first step: A more detailed descripaon of two dimensional distribuaons and the recoiling final state requires modeling the Fermi moaon in more detail and in paracular the distribuaon of removal energies. The TE component has a different shape in removal energy than the independent nucleon process. It has a wider distribuaon in removal energy. There is a larger TE enhancement both a low removal energy (1p1h) and at larger removal energy (2p2h). The 2p2h process (20% of the cross secaon) has an addiaonal proton in the final state ( with P of 250-500 MeV/c). A. Bodek 22

Ps A- 1 P f 1p1h Neutrino on A=12 e binding 8 MeV e coulomb 9 MeV P i = - P s K F =0.22 GeV <P s2 > = (3/5) K F 2 = 0.029 GeV 2 <KE spectator >= 1.5 MeV E i = M A sqrt [M * A- 1 2 +Ps 2 ] M n - e binding <KE spectator > - e coulomb M n - 8 MeV 1.5 MeV - 9 MeV M n - <18.5 MeV> = M n <Δ 1p1h > 1p1h Single Nucleon Process * Iniaal state bound neutron becomes a proton leaving a recoil A- 1 spectator nucleus with one hole.

A- 2 - Ps 2p2h P f Neutrino on A=12 e binding 8 MeV e coulomb 9 MeV P i = - P s K F =0.22 GeV P s >K F <KE proton- spectator > = 106 MeV M A- 2* * =M A - M n - M p +2e binding E i = M A M ** A- 2 - sqrt [ M p 2 +Ps 2 ] M n - 2e binding KE proton- spectator e coulomb ** = M n 16 MeV KE proton- spectator 9 MeV = M n 25 MeV KE proton- spectator = M n <131 MeV> = M n <Δ 2p2h > 2p2h Produced through MEC, or isobar or SRC, or FSI process Iniaal state bound neutron becomes a proton Leaving a staaonary A- 2 nucleus with two holes and recoil spectator 2 nd proton. MEC Leads to Transverse Enhancement

JLAB measures that about 20% of the.me, the sca1ering is from 2p2h process and 80% of the.me from 1p1h process. )*+,-./0-+12+3$ )$!"(#$ *+,%-./,%0"123%+,43"567,.68492+" ":;<""=>?@A<<@"$%&" #!$ )24*5/6317,3*$8-9%:;<-=9#>$!"('$ )24*5/6317,3*$8-9?:;<-=9#>$!"(&$ #$ )24*5/6317,*$8-9%:@<-=9&>$!"(%$ *+,-./01.,23,4$!"#$!"($!"##$ *35+607428-4+$ 9.:%;<=.>:)?$!"!#$!"#'$!"#&$ *35+607428-4+$ 9.:@;<=.>:)?$!"!!#$ *+,%-./,"012.314/5+-"678"" 9:;<=88<"$%&"!$!"%$!"&$!"'$!"($ #$!"#$%&'()"!"#%$!"#$!$!"%$!"&$!"'$!"#$ )$!"#$%&'()" *35+607428-+$ 9.:%;A=.>:&?$

What does this do to the NOMAD measurements of QE scadering Average efficiency for P>0.4 GeV/c protons is 48%. 2p2h with P>0.25 GeV/c is 20% 2p2h with P>0.4 GeV/c is 10% Since 10% of events have a proton with P>0.4 GeV. This leads to rejecaon of 5% of QE events. ( 10-38 cm 2 ) 1.6 1.4 1.2 1 - + n p +! MiniBooNE, C Nomad, C Martini et al. Therefore, NOMAD cross secaon may be underesamated by 5% Beder agreement with TE model ) ( 10-38 cm 2 1.2 1 0.8 + + p n +! Nomad, C Martini et al. 0.8 0.6 0.4 0.6 0.4 0.2 M A =1.014 M A =1.30 V Tranv Enhance in G M, M A =1.014 0-1 10 1 10 E 2 10 (GeV) 0.2 M A =1.014 M A =1.30 V Trans Enhance in G M, M A =1.014 0-1 2 10 1 10 10 E (GeV)

Conclusions The transverse enhancement (TE) observed in electron scadering experiments explains much of the Axial Mass Anomaly. The enhancement is predominantly at low Q 2, so it has a greater effect on the cross secaons at low energy. The same structure funcaons and form factors describe low energy and high energy data (as expected). Therefore, high energy experiments need to include TE in modeling acceptance/efficiency correcaons. The reason for the difference in the fits to dσ/dq 2 at low energy and high energy is the limited range of accessible Q 2 (Q 2 max) for E<1 GeV. Including TE (to first order) in exisang neutrino MC generators is simple to do (by a modificaaon of GMP and GMN for bound nucleons) We also need to include the 2p2h final state in neutrino Monte Carlos per measurements from Jlab. TE should be seen in QE dσ/dq2 data currently collected by the MINERvA experiment at Fermilab over a wide range of energies More precise L and T vector structure funcaons and form factors on nuclear targets (and TE) will be available soon from Jlab JUPITER- Will provide much needed input to neutrino MC generators. More at: Bodek, Budd, Christy Eur.Phys.J.C71:1726,2011 arxiv:1106.0340[hep- ph] A. Bodek

Backup A. Bodek 28

Contributions to Quasi-elastic " Total for Neutrino 12!10-39 10 8 6 4 2 " 1 " 2 " 3 " 4 " 5 " W2 " Total 0-2 -4 0 1 2 3 4 5 6 7 8 12-39 "10 with No Transverse-Enhanced W3 for Neutrino Contributions to Quasi-elastic! Total E (GeV) 10 8 6 4 2! 1! 2! 3! 4! 5! W2! Total 0-2 -4 0 1 2 3 4 5 6 7 8 A. Bodek E (GeV) 29

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2 ratio d /dq 2 1.8 1.6 Q 2 dependence of Raao to Independent nucleons with M A =1.014 + n p +!, E =3 GeV - E=3 GeV E=1 GeV M A =1.3 K2K,T2K MINIBOONE M A =1.3 1.4 1.2 Trans Enhance looks like MA<1.014 for Q2>0.4 1 M A =1.014 (M A =1.30)/(M A =1.014) V (Tranv Enhance in G M, M A =1.014)/(m V =0.84, M A =1.014) 0.8 0 0.5 1 1.5 2 2.5 2 Q (GeV/c) 2 A. Bodek All predicaons include Pauli Blocking. 31

( 10-38 cm 2 ) 1.2 1 + + p n +! Nomad, C Martini et al. 0.8 0.6 0.4 0.2 M A =1.014 Note: NOMAD needs to include TE in modeling the acceptance/efficiency correcaons for stringent cuts used to reduce background M A =1.30 V Trans Enhance in G M, M A =1.014 0-1 2 10 1 10 10 (GeV) A. Bodek 32 E

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Ra.o of cross sec.ons to independent nucleon model with free nucleon form factors and M A =1.014 M A =1.3 predicts 35% increase in cross sec.ons for neutrinos and 30% for an.neutrinos at high energies (> 3 GeV) Transverse Enhancement predicts 15% increase in cross sec.ons for both neutrinos and an.neutrinos at high energies (>3 GeV) At low energies (<1 GeV), Transverse Enhancement predicts that the increase in an.neutrinos is smaller than the increase for neutrinos. All predicaons include Pauli Blocking. A. Bodek 37

2 ratio d /dq 2 1.8 1.6 1.4 + n p +!, E =3 GeV - Raao to M A =1.014 (mostly independent of energy. Q2 max = 3 GeV2 for E=2 GeV. Plosng the raao of dn/dq2 (without even knowing the flux in detail) to dn/dq2 for MA=1.014 should look like this plot (as long as data for neutrino energies below 2 GeV is removed). 1.2 1 (M A =1.30)/(M A =1.014) V (Tranv Enhance in G M, M A =1.014)/(m V =0.84, M A =1.014) 0.8 0 0.5 1 1.5 2 2.5 2 Q (GeV/c) 2 The small energy dependent correcaons an be included with a rudimentary knowledge of the flux. This can be tested in MINERvA ( easier to do with neutrinos then with ananeutrinos) A. Bodek 38

( 10-38 cm 2 ) 1.6 1.4 1.2 1 Total QE cross secaons on Carbon (per neutron) + n p +! - MiniBooNE, C Nomad, C M A =1.30 transverse enhancement 0.8 M A =1.014 0.6 0.4 M A =1.014 Independent Nucleon model 0.2 M A =1.30 Large M A independent nucleon model V Tranv Enhance in G M, M A =1.014 0 0 1 2 3 4 5 6 7 8 9 10 A. Bodek 39 All predicaons include Pauli Blocking. E (GeV)

=Transverse response minus longitudinal response. Q 2 =0.09 GeV2 Q 2 =0.14 GeV2 Q 2-0.33 GeV2 QE region 0.5 1.2 Integrate excess to 0.5, esamate missing high side tail, extract raao R T (raao to universal response A. Bodek funcaon) and study its Q 2 dependence Pion producaon (Δ) with Fermi moaon 40

RADIATIVE CORRECTIONS In order to do the radiaave correcaons for all Jlab s experiments one needs to know electron scadering cross secaons over a wide range of energies and Q2. Bosted and Christy published a fit that describes e- H and e- D data in the Jlab range (using data from a wide range of experiments) The Bosted- Christy fits were extended to fit nuclear targets by Bosted and Mamyan. Data from several experiments on nuclear targets are included in the fits, including preliminary data from Jlab E04-001, the QE region is described using super- scaling model of Sick, Donnelly, Maieron (nucl- th/0109032). A. Bodek 41