Pion-Nucleon Analysesof

Richard A. Arndt&

L. David Roper1967-1990

Department of PhysicsVirginia Polytechnic Institute and State University

Dedication to Richard Allen Arndt

This talk is dedicated to my colleague and friend, Richard

Allen Arndt (1933-2010), without whose work and

support my work would have not been possible.

Dedication to Michael J. Moravcsik and Bernard T. Feld

This talk is also dedicated to my mentors, Michael J. Moravcsik (1928-1989) and Bernard T. Feld (1920-1993).

Bernie initiated and guided the pion-nucleon analysis program at MIT and Mike made it possible at LLL.

http://arts.bev.net/roperldavid/roperres.htm

Strong Interaction between Richard Allen Arndt & L. David Roper

• Summer 1962, LLL: Arndt (physicist/programmer), Roper (summer physicist) in Particle Physics Group of Michael J. Moravcsik, Lawrence Livermore Laboratory.

• Summer 1963, LLL: Arndt & Roper (summer physicist)

• 1963-1965, LLL: Arndt & Roper (postdoc in Particle Physics Group of Michael J. Moravcsik)

• 1967-1990, VPI&SU: Arndt & Roper (professors)

Others Who Helped

• William M. Layson, precursor pion/nucleon analysis for MIT PhD thesis with Bernard T. Feld

• Robert M. Wright, LLL programmer/physicist• Eldon J. Halda, LLL programmer• Burton J. Moyer (1912-1973), LBL particle

physics group, for sharing many data before publication

Pi-N Postdocs & PhD Students VPI&SU

• Roger H. Hackman (pd)• Von S. Zidell (pd)• D. Mark Manley (pd)• Ronald L. Workman (pd)• Robert L. Shotwell (PhD)• John M. Ford (PhD)

Richard Arndt’s Contributions

• Developed the nucleon-nucleon partial-wave analysis code at LLL.

• Helped Robert Wright convert the NN code for Pi-N analysis.

• Insisted on energy-dependent analyses symbiosis with single-energy analyses to get around the ambiguity problem.

• Always was available for deciding what to do next.

Richard Arndt’s Contributions• At VPI&SU Dick created every computer

program and changes that I suggested and developed many ways to improve the analyses, while I ran the pi-N programs, managed grants, wrote the papers and invented the acronyms (CAPS & SAID).

• Dick continued the pion-nucleon analyses after I became department head (1990).

• Dick took the pion-nucleon analysis to GWU after he retired from VPI&SU (1998).

Computers Used for Analyses• IBM 7090 (1959 LLL): (transistorized IBM 709)– 36-bit word, 32k words (0.144 Mbytes) address space,

0.459 MHz processor• IBM 7094 (1962 LLL):– Registers increased from 3 to 7– Introduced double-precision floating point

• CDC 3600 (1963 LLL): 48-bit word, 32k words (0.192 Mbytes), 0.7 MHz

• CDC 6600 (1964 LLL): 60-bit word, 128k words (0.96 Mbytes), 10 MHz

• IBM 7040 (1967 VPI&SU): lower-cost sibling of 7090• Currently on my desk (for comparison):

Intel Core i7 975: 64-bit word, 12 Gbytes address space, 3.33 GHz four-double-core processors

IBM 7094 Console

One could watch the register lights and see the program move from one part of the calculation to another.

Computing• Two boxes of punched cards read into the

computer for each run; several runs per day. ~3/4th of the cards were data.

• Allowed to run the IBM-7094s ourselves during lunch hours while the operators had lunch. Good for short runs.

• Spent several nights with Dick Arndt running IBM-7090s at LBL to get more computing time. Good for long “interactive” runs by watching register lights.

Reasons Why the Analysis Should Fail• There are not enough data (over 1000).• There are too many data (over 1000).• You can fit any data set with 100

parameters; so what will be learned?• There is no existing computer powerful

enough to handle >1000 data and ~100 variable parameters.

• “The great pleasure in life is doing what people say you cannot do”

With a Lotta Bit of Luck

• Layson/Feld pi-N analysis at MIT/CERN• Roper 1962 summer job at LLL with its

powerful computers• Moravcsik, Arndt, Noyes & MacGregor N-N

analysis at LLL• Robert Wright interest in porting N-N code to

pi-N• Richard Arndt call to move with him to

VPI&SU

Comparison of Number of Data• Original Roper analysis to Tlab=700 MeV:– Pi+: σ(θ): ~400; P(θ): 40; R(θ): 0; A(θ): 0– Pi-: σ(θ): ~500; P(θ): 48; R(θ): 0; A(θ): 0– CX: σ(θ): 190 ; P(θ): 1; R(θ): 0; A(θ): 0– All: σ(θ): 1171; P(θ): 89; R: 0; A: 0

• Current GWU analysis to Tlab=3000 MeV– Pi+: σ(θ): 9197; P(θ): 2899; R(θ): 48; A(θ): 48– Pi-: σ(θ): 9726; P(θ): 2633; R(θ): 60; A(θ): 63– CX: σ(θ): 5935; P(θ): 302; R(θ): 0; A(θ): 0– All: σ(θ): 24,858; P(θ): 5834; R(θ): 108; A(θ): 111

Roper MIT/LLL Thesis

Breit-Wigner resonance for P33 & D13.

P11 parametrization: PRL 12, 340 (1964)

Original parametrization

Parametrization to allow resonance

Final Roper P11 ParametrizationRoper, Wright & Feld, Phys. Rev. 138, B190 (1965)

13 parameters

Interesting Results

• Copious Bevatron π-p→π0n σ(θ) data for 4 energies from 500-700 MeV Tlab and 20 angles [Phys. Rev. 156, 1415 (1967)] were accurately predicted by the MIT/LLL analysis within experimental error bars.

• Some σ(θ) data were shown to be incorrect.

Competing Pi-N Analyses

• Bransden, O’Donnell & Moorhouse, Phys. Letters 11, 339 (1964)

• Auvil, Donnachie, Lea & Lovelace, Phys. Letters 12, 76 (1964)

• Hull & Lin, Phys. Rev. 139, B630 (1965)• Bareyre, Bricman, Stirling & Villet, Phys.

Letters 18, 342 (1965)

It was a close race!

P11 Comparison 1965 to 2010

P11 Comparison 1965 to 2010

P11 Comparison 1965 to 2010

P11 Amplitude (2010)http://gwdac.phys.gwu.edu/analysis/pin_analysis.html

S11 Comparison 1965 to 2010

D13 Comparison 1965 to 2010

Pi- Total Cross Section (GWU)

P11 Shoulder

I=1/2 Total Cross Section (GWU)

P11 Shoulder

I=1/2 Total Cross Section

I=1/2 Total Cross Section

I=1/2 Total Cross Section

P11 First Pole (GWU)http://gwdac.phys.gwu.edu/analysis/pin_analysis.html

P11 Second Pole (GWU)

Final Roper P11 Parametrization

13 parameters

That is really ugly!!

New P11 Parametrization

Parameters reduced from 13 to 7!

Fit to GWU P11

Fit to GWU P11

Two-Resonances P11 Parametrization to 3000 MeV Tlab (2600 total cm energy W)

Two-Resonances P11 Parametrization to 3000 MeV Tlab

Two-Resonances P11 Parametrization to 3000 MeV Tlab

Widths for Higher Partial Waves

Fit to GWU D13

Fit to GWU D15

Fit to GWU F15

Fit to GWU G17

Fit to GWU F37

Tribute to Richard Allen Arndt

As Dick said in his autobiography, he had a “gift”. I had the good fortune to closely observe him exercise his “gift” in many ways and to greatly benefit from his “gift”.

More Details about MIT/LLL & the Rutherford Pion-Nucleon Analyses and

Their Relationship to Other Analyses

http://arts.bev.net/roperldavid/roperres.htm The Development of Pion-Nucleon Scattering Analysis

R. Gordon Moorhouse & L. David Roper